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