The problem statement, all variables and given/known data Let a, b, s, t be integers with s, t > 0. What conditions must s, t satisfy if the following statement is true: If a = b (mod s) and a = b (mod t), then a = b (mod st). The attempt at a solution If s | a, s | b, t | a and t | b, then st | a and st | b if and only if s, t are relatively prime. This is as far as I've gone. How should I continue?