Can anybody please check my working on this elementary number theory problem?
If there are solutions to $21x+15y=93$ find them.
Since gcd$(21,15)=3|93$, there are solutions to the Diophantine equation.
gcd$(21,15)=3$, by the extended Euclidean algorithm, we can write $3=-2\times21+3\times15$. Then $31\times3=31\times(-2\times21+3\times15)=-62\times21+93\times15$.
So the only solution is $x=-62$ and $y=93$? Is there any other solutions?
I don't really know any other useful theorems to solve this problem. Can anybody please give some help?