Question

For a natural umber a, let aZ be the set of all integer multiples of a. Prove that for all a, b in the set of natural numbers, a=b iff AZ=bZ

Answer 1

Let there be a and b in the set of natural numbers such as aZ=bZ.
We have that a is in aZ and therefore in bZ so b|a.
We have that b is in bZ and therefore in aZ so a|b.
Since a,b>0 a=b.