68 + Interview Questions in Basic Concepts In Number Theory And Finite Fields in Cryptograph & Network Security Page 1 InterviewSolution

1.	The product of monic polynomials is monic.(a) True(b) False(c) Can’t Say(d) None of the mentionedThis question was addressed to me in an online interview.I want to ask this question from Polynomial and Modular Arithmetic- III topic in chapter Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» RIGHT answer is (a) TRUE Easiest EXPLANATION: This is ALWAYS true over a FIELD.

Discussion

2.	The polynomial x^4+1 can be represented as –(a) (x+1)(x^3+x^2+1)(b) (x+1)(x^3+x^2+x)(c) (x)(x^2+x+1)(d) None of the mentionedI have been asked this question in a national level competition.Enquiry is from Polynomial and Modular Arithmetic- III in portion Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» The CORRECT OPTION is (d) NONE of the mentioned For EXPLANATION: (x^4+1) = (x+1)(x^3+x^2+x+1).

Discussion

3.	If f(x)=x^7+x^5+x^4+x^3+x+1 and g(x)=x^3+x+1, find f(x) – g(x).(a) x^7+x^5+x^4+x^3(b) x^6+x^4+x^2+x(c) x^4+x^2+x+1(d) x^7+x^5+x^4This question was posed to me in my homework.I'd like to ask this question from Polynomial and Modular Arithmetic- III topic in chapter Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» RIGHT choice is (d) x^7+x^5+x^4 For EXPLANATION I would SAY: Perform MODULAR subtraction.

Discussion

4.	Find the HCF/GCD of x^6+x^5+x^4+x^3+x^2+x+1 and x^4+x^2+x+1.(a) x^4+x^3+x^2+1(b) x^3+x^2+1(c) x^2+1(d) x^3+x^2+1The question was posed to me during an internship interview.This interesting question is from Polynomial and Modular Arithmetic in section Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» Correct choice is (B) x^3+x^2+1 To ELABORATE: Use Euclidean ALGORITHM and find the GCD. GCD = x^3+x^2+1.

Discussion

5.	If f(x)=x^3+x^2+2 and g(x)=x^2-x+1, find: f(x) + g(x)(a) x^3+2x^2-x+3(b) x^3+x^2+3(c) x^3+x+1(d) x^2+2x+4This question was posed to me in an online quiz.My query is from Polynomial and Modular Arithmetic- I in division Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» Right OPTION is (a) x^3+2x^2-x+3 The best I can explain: We GET the SOLUTIONS via basic polynomial addition.

Discussion

6.	What do the above numbers correspond to?0 1 2 3 40 4 3 2 10 1 2 3 4– 1 3 2 4(a) Both Additive Inverses(b) Both Multiplicative Inverses(c) Additive and Multiplicative Inverse respectively(d) Multiplicative and Additive Inverses respectivelyThe question was asked in examination.I want to ask this question from Polynomial and Modular Arithmetic- I topic in division Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» RIGHT option is (B) Both Multiplicative Inverses The best explanation: The top SET of NUMBERS correspond to ADDITIVE Inverses and the bottom set of numbers correspond to Multiplicative Inverse.

Discussion

7.	Multiply 00100110 by 10011110 in GF(2^8) with modulus 100011011.The result is(a) 00101111(b) 00101100(c) 01110011(d) 11101111I have been asked this question during an interview.This interesting question is from Polynomial and Modular Arithmetic- III in section Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» CORRECT option is (a) 00101111 To explain I would SAY: On performing POLYNOMIAL MULTIPLICATION with respect to modulus 100011011 we GET 00101111.

Discussion

8.	Is x^3 + 1 reducible over GF(2)(a) Yes(b) No(c) Can’t Say(d) Insufficient DataI have been asked this question in an international level competition.Question is from Polynomial and Modular Arithmetic- IV in division Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» CORRECT ANSWER is (a) Yes Explanation: REDUCIBLE: (X + 1)(x^2 + x + 1).

Discussion

9.	A Ring satisfies the properties(a) R-i to R-v(b) G-i to G-iv(c) G-i to R-v(d) G-i to R-iiiI have been asked this question by my school principal while I was bunking the class.This interesting question is from Groups Rings and Fields in portion Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» RIGHT ANSWER is (d) G-i to R-iii Explanation: A ring R denoted by {R, + , X} is a set of ELEMENTS with two binary operations addition and multiplication and SATISFY axioms G-i to R-iii.

Discussion

10.	Find the 8-bit word related to the polynomial x^6 + x^5 + x^2 + x +1(a) 00010011(b) 11000110(c) 00100110(d) 01100111This question was posed to me in exam.Question is from Polynomial and Modular Arithmetic- I in chapter Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» Correct CHOICE is (d) 01100111 The best EXPLANATION: The respective 8-bit WORD is 01100111.

Discussion

11.	Which of the following are irreducible polynomials?i) X^4+X^3ii) 1iii) X^2+1iv) X^4+X+1(a) i) and ii)(b) only iv)(c) ii) iii) and iv)(d) All of the optionsThis question was addressed to me during an interview.My question is based upon Polynomial and Modular Arithmetic in division Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» RIGHT CHOICE is (d) All of the options For EXPLANATION: All of the MENTIONED are IRREDUCIBLE polynomials.

Discussion

12.	Is x^3 + x^2 + 1 reducible over GF(2)(a) Yes(b) No(c) Can’t Say(d) Insufficient DataThis question was addressed to me in a national level competition.The question is from Polynomial and Modular Arithmetic- IV in chapter Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» The correct answer is (b) No To explain: Irreducible. On factoring this polynomial, ONE FACTOR is x and the other is (x + 1), which GIVES us the roots x = 0 or x = 1 RESPECTIVELY. By SUBSTITUTION of 0 and 1 into this polynomial, it clearly has no roots.

Discussion

13.	The sum of polynomials of degrees m and n has degree max[m,n].(a) True(b) False(c) Can’t Say(d) None of the mentionedI got this question in a national level competition.I need to ask this question from Polynomial and Modular Arithmetic- III topic in section Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» The correct option is (c) Can’t Say Easiest explanation: True when m is not equal to n; in that case the highest degree coefficient is of degree MAX[m,n]. But false in GENERAL when m = n, because the highest-degree coefficients might cancel (be ADDITIVE INVERSES).

Discussion

14.	Primitive Polynomial is also called a ____i) Perfect Polynomialii) Prime Polynomialiii) Irreducible Polynomialiv) Imperfect Polynomial(a) ii) and iii)(b) only iii)(c) iv) and ii)(d) NoneThe question was asked in an international level competition.Question is from Polynomial and Modular Arithmetic topic in portion Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» The correct ANSWER is (a) II) and III) For explanation: IRREDUCIBLE POLYNOMIAL is also called a prime polynomial or primitive polynomial.

Discussion

15.	How many numbers cannot be used in GF(p) in 2n where n=4?(a) 2(b) 5(c) 3(d) 1I had been asked this question in an international level competition.Enquiry is from Polynomial and Modular Arithmetic- I in division Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» The correct choice is (C) 3 The BEST I can explain: If n=4, the LARGEST prime less than 24 is 13. This means that we cannot use the integers 13, 14 and 15.

Discussion

16.	If f(x)=x^7+x^5+x^4+x^3+x+1 and g(x)=x^3+x+1, find f(x) x g(x).(a) x^12+x^5+x^3+x^2+x+1(b) x^10+x^4+1(c) x^10+x^4+x+1(d) x^7+x^5+x+1I have been asked this question in a national level competition.I want to ask this question from Polynomial and Modular Arithmetic in section Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» The correct CHOICE is (c) x^10+x^4+x+1 Explanation: PERFORM MODULAR MULTIPLICATION.

Discussion

17.	The multiplicative Inverse of 550 mod 1769 is(a) 434(b) 224(c) 550(d) Does not existThe question was asked in exam.This is a very interesting question from Number Theory in division Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» The CORRECT answer is (a) 434 Easiest EXPLANATION: The multiplicative INVERSE of 550 MOD 1769 is 550.

Discussion

18.	What is 11 mod 7 and -11 mod 7?(a) 4 and 5(b) 4 and 4(c) 5 and 3(d) 4 and -4The question was asked in examination.I want to ask this question from Number Theory topic in portion Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» The correct CHOICE is (d) 4 and -4 The best explanation: 11 MOD 7 = 4 ; -11 mod 7 = -4 mod 7 = 3 mod 7.

Discussion

19.	GCD(a,b) is the same as GCD(\|a\|,\|b\|).(a) True(b) FalseThe question was posed to me in homework.The origin of the question is Number Theory in section Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» CORRECT answer is (a) True Easy explanation: This is true. gcd(60,24) = gcd(60,-24) = 12.

Discussion

20.	If a\|b and b\|c, then a\|c.(a) True(b) FalseI have been asked this question by my school principal while I was bunking the class.This intriguing question originated from Number Theory in division Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» Right OPTION is (a) TRUE Explanation: The STATEMENT is true. For EX, 11\|66 and 66\|198 = 11\|198.

Discussion

21.	If f(x)=x^3+x^2+2 and g(x)=x^2-x+1, find the quotient off(x) / g(x)(a) x+3(b) x^2+4(c) x(d) x+2I have been asked this question in examination.Query is from Polynomial and Modular Arithmetic- I topic in chapter Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» Right ANSWER is (d) x+2 To EXPLAIN: We get the solution via basic POLYNOMIAL division.

Discussion

22.	A Field satisfies all the properties above from G-i to R-vi.(a) True(b) FalseI have been asked this question by my college director while I was bunking the class.Question is from Groups Rings and Fields topic in chapter Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» Right answer is (a) True To explain: A Field SATISFIES all the PROPERTIES above from G-i to R-vi and is DENOTED by {F, +, X}.

Discussion

23.	Find the 8-bit word related to the polynomial x6 + x + 1(a) 01000011(b) 01000110(c) 10100110(d) 11001010This question was posed to me by my school teacher while I was bunking the class.The origin of the question is Polynomial and Modular Arithmetic- IV topic in chapter Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» CORRECT ANSWER is (a) 01000011 Explanation: The RESPECTIVE 8-bit WORD is 01000011.

Discussion

24.	Find the inverse of (x^7+x+1) modulo (x^8 + x^4 + x^3+ x + 1).(a) x^7+x(b) x^6+x^3(c) x^7(d) x^5+1I have been asked this question in a job interview.My question is taken from Polynomial and Modular Arithmetic- III topic in section Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» Correct option is (c) x^7 For explanation I WOULD SAY: Finding the INVERSE with respect to (x^8 + x^4 + x^3+ x + 1) we get x^7 as the inverse.

Discussion

25.	If f(x)=x^3+x^2+2 and g(x)=x^2-x+1, find: f(x) x g(x)(a) x^4+x^2+2x+2(b) x^5+2x^3+2x+3(c) x^5+3x^2-2x+2(d) x^4+x^2+x+1The question was posed to me by my college director while I was bunking the class.I would like to ask this question from Polynomial and Modular Arithmetic- I topic in section Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» Right choice is (C) x^5+3x^2-2x+2 Easy explanation: We get the SOLUTION VIA BASIC POLYNOMIAL multiplication.

Discussion

26.	If f(x)=x^4+x^3+2 and g(x)=x^3-x+6, find: f(x) + g(x)(a) 2x^4+2x^3+x+8(b) x^4+2x^3-x+8(c) x^4+x^2+x+8(d) x^4+x^3+8The question was posed to me in an interview.Enquiry is from Polynomial and Modular Arithmetic- I in chapter Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» Correct ANSWER is (B) x^4+2x^3-x+8 To EXPLAIN I WOULD say: Perform polynomial addition.

Discussion

27.	On multiplying (x^6+x^4+x^2+x+1) by (x^7+x+1) in GF(2^8) with irreducible polynomial (x^8 + x^4 + x^3 + x + 1) we get(a) x^7+x^6+ x^3+x^2+1(b) x^6+x^5+ x^2+x+1(c) x^7+x^6+1(d) x^7+x^6+x+1This question was addressed to me in an internship interview.Query is from Polynomial and Modular Arithmetic in section Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» RIGHT answer is (C) x^7+x^6+1 For explanation I WOULD say: Multiply and Obtain the modulus we GET the POLYNOMIAL product as x^7+x^6+1.

Discussion

28.	Does the set of residue classes (mod 3) form a group with respect to modular addition?(a) Yes(b) No(c) Can’t Say(d) Insufficient DataI have been asked this question in an interview for job.The doubt is from Groups Rings and Fields topic in portion Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» The correct answer is (a) Yes The explanation is: Yes. The IDENTITY ELEMENT is 0, and the inverses of 0, 1, 2 are respectively 0, 2, 1.

Discussion

29.	For the group Sn of all permutations of n distinct symbols, Sn is an abelian group for all values of n.(a) True(b) FalseThe question was posed to me in a national level competition.My doubt is from Groups Rings and Fields in division Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» Right answer is (B) False For explanation I would SAY: For n>2 it does not FORM a Abelian Group.

Discussion

30.	Is S a ring from the following multiplication and addition tables?+ a b x a ba a b a a ab b a b a b(a) Yes(b) No(c) Can’t Say(d) Insufficient DataThe question was asked during an interview.The origin of the question is Groups Rings and Fields topic in division Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» Correct ANSWER is (a) Yes For explanation: S is a RING as it satisfies the PROPERTIES G-i to R-iii.

Discussion

31.	Calculate the GCD of 102947526 and 239821932 using Euclidean algorithm.(a) 11(b) 12(c) 8(d) 6The question was posed to me by my college professor while I was bunking the class.My question comes from Number Theory topic in section Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» RIGHT CHOICE is (d) 6 For EXPLANATION: GCD(102947526, 239821932) = 6.

Discussion

32.	The result of (x2 ⊗ P), and the result of (x ⊗ (x ⊗ P)) are the same, where P is a polynomial.(a) True(b) FalseI had been asked this question by my college director while I was bunking the class.Question is taken from Polynomial and Modular Arithmetic- IV in section Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» Right option is (a) True For explanation: The statement is true and this is the logic used BEHIND the MULTIPLICATION of POLYNOMIALS on a computer. This REDUCES COMPUTATION time.

Discussion

33.	(7x + 2)-(x^2 + 5) in Z_10 =(a) 9x^2 + 7x + 7(b) 9x^2+ 6x + 10(c) 8x^2 + 7x + 6(d) None of the mentionedThe question was asked in a national level competition.The doubt is from Polynomial and Modular Arithmetic- III in portion Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» Correct answer is (a) 9x^2 + 7x + 7 Easiest EXPLANATION: (7x + 2) – (x^2 + 5) in Z_10 = 9x^2 + 7x +7. We can FIND this via BASIC POLYNOMIAL arithmetic in Z_10.

Discussion

34.	The product of polynomials of degrees m and n has a degree m+n+1.(a) True(b) False(c) Can’t Say(d) None of the mentionedThis question was addressed to me in final exam.Asked question is from Polynomial and Modular Arithmetic- III in chapter Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» Right option is (B) False The best I can EXPLAIN: The product of POLYNOMIALS of degrees m and N has a degree m+n.

Discussion

35.	-5 mod -3 =(a) 3(b) 2(c) 1(d) 5This question was addressed to me in unit test.The doubt is from Polynomial and Modular Arithmetic- III in portion Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» CORRECT OPTION is (C) 1 To explain I WOULD say: -5 mod -3 = -2 mod -3 = 1 mod -3.

Discussion

36.	a(b+c) = ac+bc is the representation for which property?(a) G-ii(b) G-iii(c) R-ii(d) R-iiiI got this question in a national level competition.Origin of the question is Groups Rings and Fields topic in division Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» Right CHOICE is (d) R-iii To elaborate: a(b+c) = ac+bc represents the DISTRIBUTIVE Property.

Discussion

37.	An ‘Integral Domain’ satisfies the properties(a) G-i to G-iii(b) G-i to R-v(c) G-i to R-vi(d) G-i to R-iiiI had been asked this question in unit test.The question is from Groups Rings and Fields in portion Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» The correct CHOICE is (C) G-i to R-vi Best EXPLANATION: An ‘Integral Domain’ SATISFIES the PROPERTIES G-i to R-vi.

Discussion

38.	An Abelian Group satisfies the properties(a) G-i to G-v(b) G-i to R-iv(c) G-i to R-v(d) R-i to R-vThe question was posed to me in final exam.My question comes from Groups Rings and Fields topic in chapter Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» Correct choice is (a) G-i to G-v Best EXPLANATION: An ABELIAN group is a group that satisfies the Commutative PROPERTY ALSO.

Discussion

39.	11^7 mod 13 =(a) 3(b) 7(c) 5(d) 15This question was addressed to me in examination.Asked question is from Number Theory in chapter Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» Right ANSWER is (d) 15 The best explanation: The CORRECT answer is 2. Or in this case 15 mod 13 = 2.

Discussion

40.	Multiply the polynomials P1 = x^5 +x^2+ x) by P2 = (x^7 + x^4 +x^3+x^2 + x) in GF(28) with irreducible polynomial (x^8 + x^4 + x^3 + x + 1). The result is(a) x^4+ x^3+ x+1(b) x^5+ x^3+x^2+x+1(c) x^5+ x^4+ x^3+x+1(d) x^5+ x^3+x^2+xThe question was posed to me by my college director while I was bunking the class.The question is from Polynomial and Modular Arithmetic- III in division Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» The correct answer is (B) X^5+ x^3+x^2+x+1 Best explanation: On performing POLYNOMIAL multiplication we GET with respect to modulus (x^8 + x^4 + x^3 + x + 1) we get x^5+ x^3+x^2+x+1.

Discussion

41.	[(a mod n) – (b mod n)] mod n = (b – a) mod n(a) True(b) FalseThe question was asked by my school principal while I was bunking the class.Question is taken from Number Theory in chapter Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» RIGHT CHOICE is (b) FALSE Easy explanation: The EQUIVALENCE is false and can be checked by substituting values. The CORRECT equivalence would be [(a mod n) – (b mod n)] mod n = (a – b) mod n.

Discussion

42.	Which of the following is a valid property for concurrency?(a) a = b (mod n) if n\|(a-b)(b) a = b (mod n) implies b = a (mod n)(c) a = b (mod n) and b = c (mod n) implies a = c (mod n)(d) All of the mentionedI had been asked this question in my homework.The query is from Number Theory topic in section Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» RIGHT CHOICE is (d) All of the mentioned To elaborate: All are valid properties of CONGRUENCES and can be checked by using SUBSTITUTING VALUES.

Discussion

43.	7x = 6 mod 5. Then the value of x is(a) 2(b) 3(c) 4(d) 5The question was posed to me during an interview.I'm obligated to ask this question of Polynomial and Modular Arithmetic- III in section Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» The CORRECT answer is (b) 3 To explain I WOULD say: 7 x 3 mod 5 = 6 mod 5 = 1.

Discussion

44.	The polynomial f(x)=x^3+x+1 is a reducible.(a) True(b) FalseThis question was addressed to me in examination.Asked question is from Polynomial and Modular Arithmetic in division Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» The CORRECT ANSWER is (B) False The BEST I can explain: f(X)=x^3+x+1 is irreducible.

Discussion

45.	[(a mod n) + (b mod n)] mod n = (a+b) mod n(a) True(b) FalseI had been asked this question in homework.I need to ask this question from Number Theory topic in portion Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» The correct answer is (a) TRUE For explanation: The EQUIVALENCE is true and can be CHECKED by substituting VALUES.

Discussion

46.	Calculate the GCD of 8376238 and 1921023 using Euclidean algorithm.(a) 13(b) 12(c) 17(d) 7This question was posed to me during an internship interview.I want to ask this question from Number Theory in division Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» The CORRECT CHOICE is (a) 13 To ELABORATE: GCD(8376238, 1921023) = 13.

Discussion

47.	Calculate the GCD of 1160718174 and 316258250 using Euclidean algorithm.(a) 882(b) 770(c) 1078(d) 1225I had been asked this question in an online quiz.Question is taken from Number Theory topic in section Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» RIGHT CHOICE is (c) 1078 For explanation: GCD(1160718174, 316258250) = 1078.

Discussion

48.	The GCD of x^3 – x + 1 and x^2 + 1 over GF(3) is(a) 1(b) x(c) x + 1(d) x^2 + 1The question was asked in an online quiz.I would like to ask this question from Polynomial and Modular Arithmetic- IV topic in division Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» The CORRECT CHOICE is (a) 1 The EXPLANATION is: The GCD of x^3 – x + 1 and x^2 + 1 over GF(3) is 1.

Discussion

49.	(6x^2 + x + 3)x(5x^2 + 2) in Z_10 =(a) x^3 + 2x + 6(b) 5x^3 + 7x^2 + 2x + 6(c) x^3 + 7x^2 + 2x + 6(d) None of the mentionedThe question was asked by my college director while I was bunking the class.I'm obligated to ask this question of Polynomial and Modular Arithmetic- IV in section Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» Correct option is (B) 5x^3 + 7x^2 + 2x + 6 Best EXPLANATION: (6x^2 + x + 3)x(5x^2 + 2) in Z_10 =5x^3 + 7x^2 + 2x + 6. We can FIND this via basic polynomial arithmetic in Z_10.

Discussion

50.	A very common field in this category is GF(2) with the set {1, 2} and two operations, addition and multiplication.(a) True(b) FalseThis question was posed to me during an interview.The above asked question is from Polynomial and Modular Arithmetic- I topic in portion Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security
Answer» Right choice is (B) False Explanation: GF(2) is the set {0, 1} with two OPERATIONS, ADDITION and multiplication

Discussion

Explore topic-wise InterviewSolutions in .

Is x^3 + 1 reducible over GF(2)(a) Yes(b) No(c) Can’t Say(d) Insufficient DataI have been asked this question in an international level competition.Question is from Polynomial and Modular Arithmetic- IV in division Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security

How many numbers cannot be used in GF(p) in 2n where n=4?(a) 2(b) 5(c) 3(d) 1I had been asked this question in an international level competition.Enquiry is from Polynomial and Modular Arithmetic- I in division Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security

The multiplicative Inverse of 550 mod 1769 is(a) 434(b) 224(c) 550(d) Does not existThe question was asked in exam.This is a very interesting question from Number Theory in division Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security

What is 11 mod 7 and -11 mod 7?(a) 4 and 5(b) 4 and 4(c) 5 and 3(d) 4 and -4The question was asked in examination.I want to ask this question from Number Theory topic in portion Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security

GCD(a,b) is the same as GCD(|a|,|b|).(a) True(b) FalseThe question was posed to me in homework.The origin of the question is Number Theory in section Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security

If a|b and b|c, then a|c.(a) True(b) FalseI have been asked this question by my school principal while I was bunking the class.This intriguing question originated from Number Theory in division Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security

If f(x)=x^3+x^2+2 and g(x)=x^2-x+1, find the quotient off(x) / g(x)(a) x+3(b) x^2+4(c) x(d) x+2I have been asked this question in examination.Query is from Polynomial and Modular Arithmetic- I topic in chapter Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security

-5 mod -3 =(a) 3(b) 2(c) 1(d) 5This question was addressed to me in unit test.The doubt is from Polynomial and Modular Arithmetic- III in portion Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security

a(b+c) = ac+bc is the representation for which property?(a) G-ii(b) G-iii(c) R-ii(d) R-iiiI got this question in a national level competition.Origin of the question is Groups Rings and Fields topic in division Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security

An ‘Integral Domain’ satisfies the properties(a) G-i to G-iii(b) G-i to R-v(c) G-i to R-vi(d) G-i to R-iiiI had been asked this question in unit test.The question is from Groups Rings and Fields in portion Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security

An Abelian Group satisfies the properties(a) G-i to G-v(b) G-i to R-iv(c) G-i to R-v(d) R-i to R-vThe question was posed to me in final exam.My question comes from Groups Rings and Fields topic in chapter Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security

11^7 mod 13 =(a) 3(b) 7(c) 5(d) 15This question was addressed to me in examination.Asked question is from Number Theory in chapter Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security

[(a mod n) – (b mod n)] mod n = (b – a) mod n(a) True(b) FalseThe question was asked by my school principal while I was bunking the class.Question is taken from Number Theory in chapter Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security

7x = 6 mod 5. Then the value of x is(a) 2(b) 3(c) 4(d) 5The question was posed to me during an interview.I'm obligated to ask this question of Polynomial and Modular Arithmetic- III in section Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security

The polynomial f(x)=x^3+x+1 is a reducible.(a) True(b) FalseThis question was addressed to me in examination.Asked question is from Polynomial and Modular Arithmetic in division Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security

[(a mod n) + (b mod n)] mod n = (a+b) mod n(a) True(b) FalseI had been asked this question in homework.I need to ask this question from Number Theory topic in portion Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security

Calculate the GCD of 8376238 and 1921023 using Euclidean algorithm.(a) 13(b) 12(c) 17(d) 7This question was posed to me during an internship interview.I want to ask this question from Number Theory in division Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security

Calculate the GCD of 1160718174 and 316258250 using Euclidean algorithm.(a) 882(b) 770(c) 1078(d) 1225I had been asked this question in an online quiz.Question is taken from Number Theory topic in section Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security

The GCD of x^3 – x + 1 and x^2 + 1 over GF(3) is(a) 1(b) x(c) x + 1(d) x^2 + 1The question was asked in an online quiz.I would like to ask this question from Polynomial and Modular Arithmetic- IV topic in division Basic Concepts in Number Theory and Finite Fields of Cryptograph & Network Security