Friday, 1 September 2017

quadratics - Finding all pairs of integers that satisfy a bilinear Diophantine equation

The problem asks to "find all pairs of integers $(x,y)$ that satisfy the equation $xy - 2x + 7y = 49$.



So far, I've got



\begin{align}
xy - 2x + 7y &= 49 \\
x\left(y - 2\right) + 7 &= 49
\\
y &\leq 49
\end{align}




I can't get any further. Any help?

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