59 + Interview Questions in More Number Theory in Cryptograph & Network Security Page 1 InterviewSolution

1.	The inverse of 37 mod 49 is –(a) 23(b) 12(c) 4(d) 6This question was addressed to me in an interview for internship.The above asked question is from Number Theory in portion More Number Theory of Cryptograph & Network Security
Answer» Correct OPTION is (C) 4 Easiest EXPLANATION: 37^-1 MOD 49 = 4.

Discussion

2.	How many primitive roots are there for 19?(a) 4(b) 5(c) 3(d) 6I got this question in an online interview.This interesting question is from Number Theory topic in section More Number Theory of Cryptograph & Network Security
Answer» The CORRECT option is (d) 6 To explain: 2, 3, 10, 13, 14, 15 are the primitive roots of 19.

Discussion

3.	x^7 = 17 (mod 29)(a) x = 8, 9, 12, 13, 15, 24, 28 (mod 29)(b) x = 8, 10, 12, 15, 18, 26, 27 (mod 29)(c) x = 8, 10, 12, 15, 17, 24, 27 (mod 29)(d) x = 8, 9, 13, 15, 17, 24, 28 (mod 29)I have been asked this question by my college director while I was bunking the class.I would like to ask this question from Number Theory in chapter More Number Theory of Cryptograph & Network Security
Answer» The correct choice is (B) x = 8, 10, 12, 15, 18, 26, 27 (mod 29) The explanation: On SOLVING we get x = 8, 10, 12, 15, 18, 26, 27 (mod 29).

Discussion

4.	How many primitive roots are there for 25?(a) 4(b) 5(c) 7(d) 8The question was posed to me during an interview.This is a very interesting question from Number Theory in division More Number Theory of Cryptograph & Network Security
Answer» Correct OPTION is (d) 8 Explanation: 2, 3, 8, 12, 13, 17, 22, 23 are the PRIMITIVE roots of 25.

Discussion

5.	Find the solution of x^2≡ 2 mod 11 has a solution.(a) True(b) FalseThe question was posed to me in semester exam.I want to ask this question from Number Theory topic in portion More Number Theory of Cryptograph & Network Security
Answer» Correct ANSWER is (b) False Easy EXPLANATION: 2 is a QNR.

Discussion

6.	Find a number x between 0 and 28 with x^85 congruent to 6 mod 35.(a) 6(b) 32(c) 8(d) 28The question was posed to me in a national level competition.My question is based upon Number Theory topic in section More Number Theory of Cryptograph & Network Security
Answer» RIGHT OPTION is (a) 6 Easy explanation: USE Eulers Theorum.

Discussion

7.	7^(3+j) mod 19 =(a) 7^j mod 19(b) 1 mod 19(c) 7^3 + 7^j mod 19(d) All of the mentioned are trueI had been asked this question during a job interview.This is a very interesting question from Number Theory topic in division More Number Theory of Cryptograph & Network Security
Answer» The correct CHOICE is (a) 7^j mod 19 To explain I would say: 7^(3+j)mod 19 = 7^3 * 7^j mod 19 = 7^j mod 19 ( since 7^3 mod 19 = 1 ).

Discussion

8.	7^3 mod 19 =(a) 18(b) 1(c) 14(d) 12The question was asked by my school teacher while I was bunking the class.This interesting question is from Number Theory topic in chapter More Number Theory of Cryptograph & Network Security
Answer» Correct CHOICE is (B) 1 Best EXPLANATION: 7^3 MOD 19 = 1.

Discussion

9.	The group G = is always cyclic.(a) True(b) FalseI had been asked this question in an online quiz.Query is from Number Theory topic in division More Number Theory of Cryptograph & Network Security
Answer» CORRECT ANSWER is (a) True To EXPLAIN I WOULD say: G = is always cyclic.

Discussion

10.	n is prime if and only if n divides (2^n – 2).(a) True(b) FalseThis question was posed to me in homework.My question is based upon Number Theory topic in portion More Number Theory of Cryptograph & Network Security
Answer» Right option is (B) False To elaborate: This isn’t TRUE for all cases. TAKE for example 341 which is NON PRIME.

Discussion

11.	Which of the below properties are correct? Consider the following Logarithmic Properties – i) y = x(log_x(y)) ii) log_x(1) = 1 iii) log_x(x) = 0 iv) log_x(yz) = log_x(y) + log_x(z) v) log_x(yr) – r x log_x(y)(a) 1st 2nd and 4th(b) 2nd 3rd and 5th(c) 2nd 4th and 5th(d) 1st 4th and 5thThe question was asked in exam.I would like to ask this question from Number Theory in chapter More Number Theory of Cryptograph & Network Security
Answer» Right OPTION is (d) 1st 4th and 5th Easy explanation: log_x(1) = 0 ; log_x(x) = 1 are the correct VERSIONS of ii) and III).

Discussion

12.	What is the Discrete logarithm to the base 13 (mod 19) for a =13?(a) 14(b) 1(c) 8(d) 17This question was addressed to me in class test.My question is based upon Number Theory in chapter More Number Theory of Cryptograph & Network Security
Answer» CORRECT CHOICE is (b) 1 Easiest explanation: log_13(13) MOD 19 = 1.

Discussion

13.	ᶲ(19)=(a) 14(b) 13(c) 18(d) 17I have been asked this question during an interview for a job.My query is from Number Theory topic in chapter More Number Theory of Cryptograph & Network Security
Answer» The CORRECT CHOICE is (C) 18 Explanation: 19 is a prime no. HENCE ᶲ(19)= 18.

Discussion

14.	gcd( 18,300) =(a) 4(b) 12(c) 8(d) 6This question was posed to me during an interview for a job.The query is from Number Theory in portion More Number Theory of Cryptograph & Network Security
Answer» Correct option is (d) 6 The explanation is: GCD( 18,300) = 6. Find the COMMON FACTORS to compute GCD/HCF.

Discussion

15.	Find a number ‘a’ between 0 and 72 with ‘a’ congruent to 9794 mod 73.(a) 53(b) 29(c) 12(d) 37I had been asked this question during an online exam.The doubt is from Number Theory topic in section More Number Theory of Cryptograph & Network Security
Answer» Right CHOICE is (c) 12 The EXPLANATION: USE Fermats THEORUM.

Discussion

16.	Find the order of the group G = ?(a) 4(b) 5(c) 6(d) 2The question was asked in an interview.I need to ask this question from Number Theory topic in section More Number Theory of Cryptograph & Network Security
Answer» RIGHT answer is (a) 4 To ELABORATE: It can be OBTAINED USING Euler Phi function, i.e. f(n).

Discussion

17.	ᶲ(231)=(a) 230(b) 60(c) 80(d) 120I got this question during an online interview.The query is from Number Theory topic in division More Number Theory of Cryptograph & Network Security
Answer» RIGHT CHOICE is (d) 120 For explanation: ᶲ(231) = ᶲ(3) x ᶲ(7) x ᶲ(11) = 2 x 6 x 10 = 120.

Discussion

18.	What is the period of 7^mmod 19?(a) 2(b) 3(c) 4(d) 5The question was posed to me in quiz.The query is from Number Theory in portion More Number Theory of Cryptograph & Network Security
Answer» The correct option is (b) 3 For EXPLANATION: PERIOD is 3. It is the smallest POSITIVE INTEGER for which 7^m mod 19 = 1.

Discussion

19.	If a group has primitive roots, it is a cyclic group(a) True(b) FalseThe question was posed to me during an interview.I'd like to ask this question from Number Theory in section More Number Theory of Cryptograph & Network Security
Answer» The CORRECT ANSWER is (a) True The explanation: YES, a group which has primitive roots is a CYCLIC group.

Discussion

20.	ᶲ(440)=(a) 200(b) 180(c) 160(d) 220I have been asked this question in my homework.The above asked question is from Number Theory in portion More Number Theory of Cryptograph & Network Security
Answer» Correct choice is (c) 160 Explanation: ᶲ(440) = ᶲ(2^3) X ᶲ(5) x ᶲ(11) = (2^3 – 2^2) x 4 x 10 = 160.

Discussion

21.	Find a number ‘a’ between 0 and 9such that ‘a’ is congruent to 7^1000 mod 10.(a) 2(b) 1(c) 3(d) 4This question was posed to me in my homework.The question is from Number Theory topic in portion More Number Theory of Cryptograph & Network Security
Answer» Correct answer is (b) 1 To EXPLAIN: Use EULERS THEORUM.

Discussion

22.	ᶲ(27)=(a) 6(b) 12(c) 26(d) 18This question was posed to me by my college director while I was bunking the class.This interesting question is from Number Theory topic in chapter More Number Theory of Cryptograph & Network Security
Answer» The CORRECT ANSWER is (d) 18 The best explanation: ᶲ(27) = ᶲ(33) = 3^3 – 3^2 = 27 – 9 = 18.

Discussion

23.	What is the Discrete logarithm to the base 2 (mod 19) for a =7?(a) 3(b) 4(c) 6(d) 9I had been asked this question in final exam.This interesting question is from Number Theory in section More Number Theory of Cryptograph & Network Security
Answer» Correct choice is (c) 6 Explanation: log_2(7) MOD 19 = 6.

Discussion

24.	17 x^2 = 10 ( mod 29 )(a) x = 3, 22 (mod 29)(b) x = 7, 28 (mod 29)(c) x = 2, 27 (mod 29)(d) x = 4, 28 (mod 29)The question was posed to me during an online exam.This interesting question is from Number Theory in section More Number Theory of Cryptograph & Network Security
Answer» Correct choice is (C) x = 2, 27 (MOD 29) The EXPLANATION is: On SOLVING we get x = 2, 27 (mod 29).

Discussion

25.	Find the solution of x^2≡ 3 mod 11(a) x ≡ -9 mod 11 andx≡ 9 mod 11(b) x ≡ 9 mod 11(c) No Solution(d) x ≡ 5 mod 11 and x ≡ 6 mod 11I got this question in final exam.The origin of the question is Number Theory in division More Number Theory of Cryptograph & Network Security
Answer» RIGHT choice is (d) x ≡ 5 mod 11 and x ≡ 6 mod 11 Easiest EXPLANATION: On FINDING the QUADRATIC congruencies we get x ≡ 5 mod 11 and x ≡ -5 mod 11.

Discussion

26.	The order of group G= , primitive roots of the group are –(a) 8 , Primitive roots- 2,3(b) 6 , Primitive roots- 5(c) 6 , Primitive roots- 2,5(d) 6 , Primitive roots- 5,7I had been asked this question by my college director while I was bunking the class.This question is from Number Theory in section More Number Theory of Cryptograph & Network Security
Answer» Right choice is (c) 6 , Primitive roots- 2,5 The EXPLANATION: \|G\| = f(9) = (32-31) = 6 G = = { 1, 2, 4, 5, 7, 8 }.

Discussion

27.	Find the solution of x^2≡ 16 mod 23(a) x = 6 and 17(b) x = 4 and 19(c) x = 11 and 12(d) x = 7 and 16This question was posed to me during an interview.The query is from Number Theory topic in chapter More Number Theory of Cryptograph & Network Security
Answer» The correct choice is (B) x = 4 and 19 To explain: a=16(16)^((23+1)/4) ≡ (16)^6≡1(QR and there is SOLUTION). x ≡ ±16(23 + 1)/4 (mod 23) ≡±4i.e. x = 4 and 19.

Discussion

28.	Find the solution of x^2≡ 15 mod 23 has a solution.(a) True(b) FalseThis question was addressed to me in homework.This key question is from Number Theory topic in portion More Number Theory of Cryptograph & Network Security
Answer» The correct CHOICE is (B) False The EXPLANATION: a=15(15)^((23-1)/2)≡(15)^11≡-1(QNR and no solution).

Discussion

29.	Euler’s Criterion can find the solution to x2 ≡ a (mod n).(a) True(b) FalseThe question was asked in semester exam.I would like to ask this question from Number Theory in chapter More Number Theory of Cryptograph & Network Security
Answer» The CORRECT choice is (b) False Explanation: EULER’s Criterion cannot find the solution to X2 ≡ a (MOD N).

Discussion

30.	GCD(n,n+1) = 1 always.(a) True(b) FalseI had been asked this question during an internship interview.This intriguing question originated from Number Theory in chapter More Number Theory of Cryptograph & Network Security
Answer» CORRECT option is (a) True To explain: If p were any prime dividing n and n + 1 it WOULD also have to divide (n + 1) – n = 1. THUS GCD of 2 consecutive numbers is ALWAYS 1.

Discussion

31.	Find the primitive roots of G = .(a) {2, 6, 8}(b) {3,6 ,9}(c) {3, 7, 8}(d) {3, 7}I got this question by my college director while I was bunking the class.My enquiry is from Number Theory in chapter More Number Theory of Cryptograph & Network Security
Answer» CORRECT option is (C) {3, 7, 8} The explanation is: Number of primitive roots = f(f(11))=f((111-110)) = f(10)= f(2). f(5) = (21-20)(51-50) = 1 x 4 = 4 The primitive roots of this set are {3, 7}.

Discussion

32.	Find the solution of x^2≡ 2 mod 11(a) No Solution(b) x ≡ 9 mod 11(c) x ≡ 4 mod 11(d) x ≡ 4 mod 11 and x ≡ 7 mod 11I have been asked this question during an online exam.This intriguing question comes from Number Theory topic in chapter More Number Theory of Cryptograph & Network Security
Answer» RIGHT ANSWER is (a) No SOLUTION Explanation: There is no solution possible on SOLVING the CONGRUENCY.

Discussion

33.	Find a number x between 0 and 28 with x^85 congruent to 6 mod 29.(a) 22(b) 12(c) 6(d) 18The question was posed to me by my college director while I was bunking the class.This key question is from Number Theory topic in chapter More Number Theory of Cryptograph & Network Security
Answer» The CORRECT CHOICE is (C) 6 Explanation: USE Fermats THEORUM.

Discussion

34.	What is the Discrete logarithm to the base 10 (mod 19) for a =7?(a) 12(b) 14(c) 8(d) 11This question was posed to me in my homework.I want to ask this question from Number Theory in portion More Number Theory of Cryptograph & Network Security
Answer» RIGHT OPTION is (a) 12 Best explanation: log_10(7) mod 19 = 12.

Discussion

35.	What is the period of 11 (mod 19)(a) 2(b) 3(c) 4(d) 5The question was asked in an international level competition.My query is from Number Theory in section More Number Theory of Cryptograph & Network Security
Answer» RIGHT ANSWER is (b) 3 To elaborate: 11^3 (mod 19) = 1.

Discussion

36.	In the group G = , when the order of an element is the same as order of the group (i.e. f(n)), that element is called the Non – primitive root of the group.(a) True(b) FalseI had been asked this question in final exam.The doubt is from Number Theory in portion More Number Theory of Cryptograph & Network Security
Answer» Correct answer is (b) False For explanation I WOULD say: Such a GROUP is CALLED the PRIMITIVE root of the group.

Discussion

37.	Find the number of primitive roots of G=?(a) 5(b) 6(c) 4(d) 10This question was posed to me in a national level competition.This interesting question is from Number Theory topic in chapter More Number Theory of Cryptograph & Network Security
Answer» The correct choice is (c) 4 Easy explanation: Number of primitive ROOTS = f(f(11))=f((111-110)) = f(10)= f(2). f(5) = (21-20)(51-50) = 1 x 4 = 4 The primitive roots of this set {2, 6, 7, 8}.

Discussion

38.	Find x for the CRT when x= 2 mod 3; x= 3 mod 5; x = 2 mod 7(a) 33(b) 22(c) 23(d) 31I got this question by my school principal while I was bunking the class.I would like to ask this question from Number Theory in portion More Number Theory of Cryptograph & Network Security
Answer» The correct choice is (c) 23 For explanation: We have M = 3 x 5 x 7 = 105; M/3 = 35; M/5 = 21; M/7 = 15. The SET of linear congruences 35 x b1 = 1 (mod 3); 21 x b2 = 1 (mod 5); 15 x b3 = 1 (mod 7) has the solutions b1 = 2; b2 = 1; b3 = 1. Then, x = 2 x 2 c 35 + 3 x 1 x 21 + 2 x 1 x 15 = 233 (mod 105) = 23.

Discussion

39.	ᶲ(41)=(a) 40(b) 20(c) 18(d) 22The question was posed to me at a job interview.Origin of the question is Number Theory topic in chapter More Number Theory of Cryptograph & Network Security
Answer» The CORRECT CHOICE is (a) 40 Explanation: 41 is a PRIME.

Discussion

40.	Find the order of the group G = ?(a) 12(b) 8(c) 13(d) 11The question was posed to me in unit test.The origin of the question is Number Theory in section More Number Theory of Cryptograph & Network Security
Answer» The correct option is (a) 12 Best explanation: \|G\| = f(21) = f(3) × f(7) = 2 × 6 =12 There are 12 elements in this group: G = = {1, 2, 4, 5, 8, 10, 11, 13, 16, 17, 19, 20}. All are relatively prime with 21.

Discussion

41.	What is the period of 9 (mod 19)(a) 12(b) 10(c) 11(d) 9The question was posed to me in an interview for internship.Asked question is from Number Theory topic in section More Number Theory of Cryptograph & Network Security
Answer» Right OPTION is (d) 9 To EXPLAIN: 9^9 (MOD 19) = 1.

Discussion

42.	ᶲ(35)=(a) 24(b) 25(c) 22(d) 18This question was addressed to me in final exam.My question is taken from Number Theory topic in division More Number Theory of Cryptograph & Network Security
Answer» RIGHT answer is (a) 24 The best explanation: ᶲ(36) = 24 = 6 x 4. These are the NUMBERS which are relatively prime– 1,2,3,4,6,8,9,11,12,13,16,17,18,19,22,23,24,26,27,29,31,33,34.

Discussion

43.	Which among the following values:17, 20, 38, and 50, does not have primitive roots in the group G = ?(a) 17(b) 20(c) 38(d) 50I got this question in an interview.I'm obligated to ask this question of Number Theory in portion More Number Theory of Cryptograph & Network Security
Answer» RIGHT option is (b) 20 To explain: The group G = has primitive roots only if N is 2, 4, PT, or 2pt ‘p’ is an odd prime and‘t’ is an integer. G = has primitive roots, 17 is a prime. G = has no primitive roots. G = has primitive roots, 38 = 2 × 19 prime. G = has primitive roots, 50 = 2 × 52 and 5 is a prime.

Discussion

44.	In the order of group G= , what is the order of element 17?(a) 16(b) 4(c) 11(d) 6The question was asked during a job interview.My doubt stems from Number Theory topic in section More Number Theory of Cryptograph & Network Security
Answer» Correct answer is (b) 4 The BEST I can explain: 17 17 9 13 1ord(17) = 4 n? 1 2 3 4 5 6 7 ORDER

Discussion

45.	ᶲ(21)=(a) 10(b) 12(c) 8(d) 14I had been asked this question in a job interview.The question is from Number Theory topic in division More Number Theory of Cryptograph & Network Security
Answer» The correct option is (b) 12 The EXPLANATION is: ᶲ(21)= 6 X 2 =12.

Discussion

46.	Find the order of group G= (a) 6(b) 9(c) 10(d) 8I got this question during an online interview.The doubt is from Number Theory in chapter More Number Theory of Cryptograph & Network Security
Answer» The correct answer is (d) 8 Easy explanation: \|G\| = f(20) = f(4) × f(5) = f(22) × f(5) = (22-21)(51-50) = 8. G = = { 1, 3, 7, 9, 11, 13, 17, 19 }.

Discussion

47.	In Zp* with (p-1) elements exactly:(a) /2 elements are QR and(b) /2 elements are QNR.(c) True(d) FalseThe question was posed to me in final exam.Enquiry is from Number Theory topic in chapter More Number Theory of Cryptograph & Network Security
Answer» The correct choice is (a) /2 elements are QR and The BEST I can explain: The STATEMENT is TRUE concerning elements of Zp* with (p-1) elements.

Discussion

48.	Find the solution of x^2≡7 mod 19(a) x≡±16 mod 23(b) x≡±11 mod 23(c) x≡±14 mod 23(d) x≡±7 mod 23This question was posed to me in semester exam.This interesting question is from Number Theory topic in division More Number Theory of Cryptograph & Network Security
Answer» Correct ANSWER is (b) x≡±11 mod 23 To elaborate: a=77^((19+1)/4)≡7^5≡1(QR and there is solution) x ≡ ±7(19 + 1)/4 (mod 19) ≡±11i.e. x = 11 and 12.

Discussion

49.	Six teachers begin courses on Monday Tuesday Wednesday Thursday Friday and Saturday, respectively, and announce their intentions of lecturing at intervals of 2,3,4,1,6 and 5 days respectively. Sunday lectures are forbidden. When first will all the teachers feel compelled to omit a lecture? Use CRT.(a) 354(b) 371(c) 432(d) 213I got this question during an interview.This intriguing question originated from Number Theory topic in chapter More Number Theory of Cryptograph & Network Security
Answer» Right OPTION is (b) 371 The explanation is: USE CRT to GET the ANSWER as 371.

Discussion

50.	Consider a function: f(n) = number of elements in the set {a: 0
Answer» The CORRECT option is (B) TOTIENT To elaborate: Such a set is KNOWN as Totient.

Discussion

Explore topic-wise InterviewSolutions in .

The inverse of 37 mod 49 is –(a) 23(b) 12(c) 4(d) 6This question was addressed to me in an interview for internship.The above asked question is from Number Theory in portion More Number Theory of Cryptograph & Network Security

How many primitive roots are there for 19?(a) 4(b) 5(c) 3(d) 6I got this question in an online interview.This interesting question is from Number Theory topic in section More Number Theory of Cryptograph & Network Security

How many primitive roots are there for 25?(a) 4(b) 5(c) 7(d) 8The question was posed to me during an interview.This is a very interesting question from Number Theory in division More Number Theory of Cryptograph & Network Security

Find the solution of x^2≡ 2 mod 11 has a solution.(a) True(b) FalseThe question was posed to me in semester exam.I want to ask this question from Number Theory topic in portion More Number Theory of Cryptograph & Network Security

Find a number x between 0 and 28 with x^85 congruent to 6 mod 35.(a) 6(b) 32(c) 8(d) 28The question was posed to me in a national level competition.My question is based upon Number Theory topic in section More Number Theory of Cryptograph & Network Security

7^(3+j) mod 19 =(a) 7^j mod 19(b) 1 mod 19(c) 7^3 + 7^j mod 19(d) All of the mentioned are trueI had been asked this question during a job interview.This is a very interesting question from Number Theory topic in division More Number Theory of Cryptograph & Network Security

7^3 mod 19 =(a) 18(b) 1(c) 14(d) 12The question was asked by my school teacher while I was bunking the class.This interesting question is from Number Theory topic in chapter More Number Theory of Cryptograph & Network Security

The group G = is always cyclic.(a) True(b) FalseI had been asked this question in an online quiz.Query is from Number Theory topic in division More Number Theory of Cryptograph & Network Security

n is prime if and only if n divides (2^n – 2).(a) True(b) FalseThis question was posed to me in homework.My question is based upon Number Theory topic in portion More Number Theory of Cryptograph & Network Security

What is the Discrete logarithm to the base 13 (mod 19) for a =13?(a) 14(b) 1(c) 8(d) 17This question was addressed to me in class test.My question is based upon Number Theory in chapter More Number Theory of Cryptograph & Network Security

ᶲ(19)=(a) 14(b) 13(c) 18(d) 17I have been asked this question during an interview for a job.My query is from Number Theory topic in chapter More Number Theory of Cryptograph & Network Security

gcd( 18,300) =(a) 4(b) 12(c) 8(d) 6This question was posed to me during an interview for a job.The query is from Number Theory in portion More Number Theory of Cryptograph & Network Security

Find a number ‘a’ between 0 and 72 with ‘a’ congruent to 9794 mod 73.(a) 53(b) 29(c) 12(d) 37I had been asked this question during an online exam.The doubt is from Number Theory topic in section More Number Theory of Cryptograph & Network Security

Find the order of the group G = ?(a) 4(b) 5(c) 6(d) 2The question was asked in an interview.I need to ask this question from Number Theory topic in section More Number Theory of Cryptograph & Network Security

ᶲ(231)=(a) 230(b) 60(c) 80(d) 120I got this question during an online interview.The query is from Number Theory topic in division More Number Theory of Cryptograph & Network Security

What is the period of 7^mmod 19?(a) 2(b) 3(c) 4(d) 5The question was posed to me in quiz.The query is from Number Theory in portion More Number Theory of Cryptograph & Network Security

If a group has primitive roots, it is a cyclic group(a) True(b) FalseThe question was posed to me during an interview.I'd like to ask this question from Number Theory in section More Number Theory of Cryptograph & Network Security

ᶲ(440)=(a) 200(b) 180(c) 160(d) 220I have been asked this question in my homework.The above asked question is from Number Theory in portion More Number Theory of Cryptograph & Network Security

Find a number ‘a’ between 0 and 9such that ‘a’ is congruent to 7^1000 mod 10.(a) 2(b) 1(c) 3(d) 4This question was posed to me in my homework.The question is from Number Theory topic in portion More Number Theory of Cryptograph & Network Security

ᶲ(27)=(a) 6(b) 12(c) 26(d) 18This question was posed to me by my college director while I was bunking the class.This interesting question is from Number Theory topic in chapter More Number Theory of Cryptograph & Network Security

What is the Discrete logarithm to the base 2 (mod 19) for a =7?(a) 3(b) 4(c) 6(d) 9I had been asked this question in final exam.This interesting question is from Number Theory in section More Number Theory of Cryptograph & Network Security

17 x^2 = 10 ( mod 29 )(a) x = 3, 22 (mod 29)(b) x = 7, 28 (mod 29)(c) x = 2, 27 (mod 29)(d) x = 4, 28 (mod 29)The question was posed to me during an online exam.This interesting question is from Number Theory in section More Number Theory of Cryptograph & Network Security

Find the solution of x^2≡ 3 mod 11(a) x ≡ -9 mod 11 andx≡ 9 mod 11(b) x ≡ 9 mod 11(c) No Solution(d) x ≡ 5 mod 11 and x ≡ 6 mod 11I got this question in final exam.The origin of the question is Number Theory in division More Number Theory of Cryptograph & Network Security

Find the solution of x^2≡ 16 mod 23(a) x = 6 and 17(b) x = 4 and 19(c) x = 11 and 12(d) x = 7 and 16This question was posed to me during an interview.The query is from Number Theory topic in chapter More Number Theory of Cryptograph & Network Security

Find the solution of x^2≡ 15 mod 23 has a solution.(a) True(b) FalseThis question was addressed to me in homework.This key question is from Number Theory topic in portion More Number Theory of Cryptograph & Network Security

Euler’s Criterion can find the solution to x2 ≡ a (mod n).(a) True(b) FalseThe question was asked in semester exam.I would like to ask this question from Number Theory in chapter More Number Theory of Cryptograph & Network Security

GCD(n,n+1) = 1 always.(a) True(b) FalseI had been asked this question during an internship interview.This intriguing question originated from Number Theory in chapter More Number Theory of Cryptograph & Network Security

Find the primitive roots of G = .(a) {2, 6, 8}(b) {3,6 ,9}(c) {3, 7, 8}(d) {3, 7}I got this question by my college director while I was bunking the class.My enquiry is from Number Theory in chapter More Number Theory of Cryptograph & Network Security

Find the solution of x^2≡ 2 mod 11(a) No Solution(b) x ≡ 9 mod 11(c) x ≡ 4 mod 11(d) x ≡ 4 mod 11 and x ≡ 7 mod 11I have been asked this question during an online exam.This intriguing question comes from Number Theory topic in chapter More Number Theory of Cryptograph & Network Security

Find a number x between 0 and 28 with x^85 congruent to 6 mod 29.(a) 22(b) 12(c) 6(d) 18The question was posed to me by my college director while I was bunking the class.This key question is from Number Theory topic in chapter More Number Theory of Cryptograph & Network Security

What is the Discrete logarithm to the base 10 (mod 19) for a =7?(a) 12(b) 14(c) 8(d) 11This question was posed to me in my homework.I want to ask this question from Number Theory in portion More Number Theory of Cryptograph & Network Security

What is the period of 11 (mod 19)(a) 2(b) 3(c) 4(d) 5The question was asked in an international level competition.My query is from Number Theory in section More Number Theory of Cryptograph & Network Security

Find the number of primitive roots of G=?(a) 5(b) 6(c) 4(d) 10This question was posed to me in a national level competition.This interesting question is from Number Theory topic in chapter More Number Theory of Cryptograph & Network Security

Find x for the CRT when x= 2 mod 3; x= 3 mod 5; x = 2 mod 7(a) 33(b) 22(c) 23(d) 31I got this question by my school principal while I was bunking the class.I would like to ask this question from Number Theory in portion More Number Theory of Cryptograph & Network Security

ᶲ(41)=(a) 40(b) 20(c) 18(d) 22The question was posed to me at a job interview.Origin of the question is Number Theory topic in chapter More Number Theory of Cryptograph & Network Security

Find the order of the group G = ?(a) 12(b) 8(c) 13(d) 11The question was posed to me in unit test.The origin of the question is Number Theory in section More Number Theory of Cryptograph & Network Security

What is the period of 9 (mod 19)(a) 12(b) 10(c) 11(d) 9The question was posed to me in an interview for internship.Asked question is from Number Theory topic in section More Number Theory of Cryptograph & Network Security

ᶲ(35)=(a) 24(b) 25(c) 22(d) 18This question was addressed to me in final exam.My question is taken from Number Theory topic in division More Number Theory of Cryptograph & Network Security

Which among the following values:17, 20, 38, and 50, does not have primitive roots in the group G = ?(a) 17(b) 20(c) 38(d) 50I got this question in an interview.I'm obligated to ask this question of Number Theory in portion More Number Theory of Cryptograph & Network Security

In the order of group G= , what is the order of element 17?(a) 16(b) 4(c) 11(d) 6The question was asked during a job interview.My doubt stems from Number Theory topic in section More Number Theory of Cryptograph & Network Security

ᶲ(21)=(a) 10(b) 12(c) 8(d) 14I had been asked this question in a job interview.The question is from Number Theory topic in division More Number Theory of Cryptograph & Network Security

Find the order of group G= (a) 6(b) 9(c) 10(d) 8I got this question during an online interview.The doubt is from Number Theory in chapter More Number Theory of Cryptograph & Network Security

In Zp* with (p-1) elements exactly:(a) /2 elements are QR and(b) /2 elements are QNR.(c) True(d) FalseThe question was posed to me in final exam.Enquiry is from Number Theory topic in chapter More Number Theory of Cryptograph & Network Security

Find the solution of x^2≡7 mod 19(a) x≡±16 mod 23(b) x≡±11 mod 23(c) x≡±14 mod 23(d) x≡±7 mod 23This question was posed to me in semester exam.This interesting question is from Number Theory topic in division More Number Theory of Cryptograph & Network Security

Consider a function: f(n) = number of elements in the set {a: 0