Solve the congruence 3x=5(mod4), x=? where k is any integer

Answer 1

Under modulo 4, we can re-write the congruence as 3x ≡ 1 (mod 4). It should be straightforward to determine the value of x (under mod 4) that satisfies this congruence via checking each of 0, 1, 2, or 3. Alternatively, if you recognize that 3 is equivalent to -1 mod 4, you can re-write this as -1x ≡ 1 (mod 4), which makes it much more direct to solve for x.