Let a, b, c be integers. Prove that ...

Question

Answer 1

Proof by contradiction

Suppose a | b, then b = ka, where k is an integer

Then bc = kac = (kc) a, as k and c are integers so is kc, therefore a | bc

So we can't have a | b

Similarly we cant have a | c, so both a | b and a|c must be false simultaneously