I tried to prove this claim, as I require it to finish one of my proofs. By definition, if a,b are integers, with [itex]a \ne 0[/itex], we say that a divides b if there exists an integer c such that b = ca. So, n divides 0 means that there exists some integer c such that n = c*0 = 0. But this would contradict the fact that n can't be zero. What is wrong with this proof?