If x is congruent to 13 modulo 17 then 7x - 3 is congruent to which nu

1.	If x is congruent to 13 modulo 17 then 7x - 3 is congruent to which number modulo 17?
Answer» x ≡ 13 (mod 17) Let p be the required number … (1) 7x – 3 ≡ p (mod 17) … (2) From (1), x – 13 = 17n for some integer M. x – 13 is a multiple of 17. x must be 30. ∴ 30 – 13 = 17 Which is a multiple of 17. From (2), 7 x 30 – 3 ≡ p (mod 17) 210 – 3 ≡ p (mod 17) 207 ≡ p (mod 17) 207 ≡ 3 (mod 17) ∴ P ≡ 3

If x is congruent to 13 modulo 17 then 7x - 3 is congruent to which number modulo 17?

Answer»

x ≡ 13 (mod 17)

Let p be the required number … (1)

7x – 3 ≡ p (mod 17) … (2)

From (1),

x – 13 = 17n for some integer M.

x – 13 is a multiple of 17.

x must be 30.

∴ 30 – 13 = 17

Which is a multiple of 17.

From (2),

7 x 30 – 3 ≡ p (mod 17)

210 – 3 ≡ p (mod 17)

207 ≡ p (mod 17)

207 ≡ 3 (mod 17)

∴ P ≡ 3