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?
2026-04-13 08:28:15.1776068895
Finding all pairs of integers that satisfy a bilinear Diophantine equation
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hint: $xy+7y = 2x+49 \implies (x+7)y = 2x+49 \implies y = \dfrac{2x+49}{x+7}= 2 + \dfrac{35}{x+7}\implies (x+7) \mid 35\implies x+7 = \pm 1, \pm 5, \pm 7, \pm 35$