Number theory: simple gcd question

  • #1

Homework Statement

If ax+by=1, then (a,b)=1.

Homework Equations

The Attempt at a Solution

I am just wondering if this is true. Because I know it is not true if ax+by=c, then (a,b)=c.

Here is a proof I came up with:

Suppose (a,b)=c, c>1.Then c|a and c|b, but then from our assumption, this implies that c|1, a contradiction.

I'm new to writing proofs so I just want to make sure I am on the right track. Thanks.
  • #2
It's ok. The proof is good.

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