# Math Help - gcd proof 1

1. ## gcd proof 1

let a,b,c belongs to integers.prove that the equation ax+by=c has integer solutions if and only if (a,b)|c.

2. Originally Posted by Deepu
let a,b,c belongs to integers.prove that the equation ax+by=c has integer solutions if and only if (a,b)|c.
This is a number theory proof. If $ax+by=c$ then we have that $(a,b)\mid ax,by\implies (a,b)\mid ax+by=c$. Try the other way.

3. Originally Posted by Drexel28
This is a number theory proof. If $ax+by=c$ then we have that $(a,b)\mid ax,by\implies (a,b)\mid ax+by=c$. Try the other way.
Thank you... but can you do this proof by the concept of division algorithm method..

4. Originally Posted by Deepu
Thank you... but can you do this proof by the concept of division algorithm method..
No. Can you?