Prove:

If , then .

My knowledge of the greatest common factor (GCD) is rather limited, but I'm thinking this will involve representing GCD expressions with linear combinations. Here is what I know:

The greatest common divisor of the nonzero integers and is the least positive integer that is a linear combination of and .

And the trivial assumption: implies there exists a number that is acommondivisor of and .

Assume .

Let .

Then divides , , and .

So , , and for some integers , , and .

Let .

Then divides and .

So and for some integers and .

(Now what?)

If this is even the correct start to this proof, I would be amazed. I imagine the next steps would involve substitution, but I'm not sure how to proceed. Any help would be appreciated!