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