For linear diophantine equation: $qx+py = c$ , where $p$ is a prime and $q$ is a natural number, why is it that if $p<q$ then there is a solution to the equation, however when $p>q$ then there is no solution to the equation?
I just don't see why either number has to be greater for there to be a solution; I'm assuming it has to do with the fact that $p$ is prime. Any help is appreciated, thanks!
$x+2y=1$ has a solution namely $x=3$, $y=-1$.