Question

Let a and b be positive integers. Let S = {ma + nb : m, n ∈ Z and ma + nb > 0}.

Answer 1

1. Prove that S is nonempty.
2. Let d be the least element of S. Prove that d|a and d|b.
3. Let c ∈ N be such that c|a and c|b. Prove that c|d.

Answer 2

@jhonyy9 would you mind taking a look at this when you get a chance