Solve the linear congruence 3x ≡ 7 mod 13 for x

Answer 1

1. Since 3 does not divide 7, you want to use 7(mod 13) to find a number that is divisible by 3 in order to solve for x.
2. 7 ≡ 20 ≡ 33 ≡ 46 ≡ .... (mod 13)

So 3x ≡ 7 is equivalent to 3x ≡ 33.

And x ≡ 11(mod 13).

Check: 7 ≡ 3·11 (mod 13)