introduction to number theory?

[^_^]

Given integers a, b, c, d, verify the following:

a | b if and only if ac | bc, where c does not equal to 0

 

[Dotty]

It's an iff proof, so technically we should do it in both directions, but I think using equivalencies throughout will suffice. I'll flip this around as well.

ac | bc bc = acn (n ) b = an (because c 0) a | b

I used the fact that x | y means the same thing as y = xn, i.e y is some integer multiple of x.