# Linear diophantine equations

1. Feb 4, 2010

### mlsbbe

Do diophantine equations ax+by =C with gcd (a,b) = 1 have a solution?

Last edited: Feb 4, 2010
2. Feb 4, 2010

### CRGreathouse

Sure. Use the CRT.

You can even get a solution in the more general case gcd(a, b) | C.