Find all integer solutions for x and y.
I can solve linear diophantine equations without a problem normally but this has me stumped.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.Sign up to join this community
Rewrite as $xy-14x-14y=0$, and then, in an analogue of completing the square, as $(x-14)(y-14)=196$.
So $x-14$ ranges over the divisors of $196$. Since $196=2^2\cdot 7^2$, $196$ has $(2)(3)(3)$ integer divisors, including the negative divisors. That gives $18$ possible values of $x$.