Solve diophantine using modulus Find all pairs of positive integers $(m, n)$ that satisfy, $mn + 3m - 8n = 59$ Using Modular arithmetic. Okay, this is a diophantine equation, where can I begin?

Hint:

I would begin by factoring as follows $$(m-8)(n+3)=59-24=35 = 1\cdot 5\cdot7$$

Now can you think of the possibilities for $m-8, n+3$? Do not forget $m, n > 0$

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_P.S. Modular arithmetic seems really unnecessary here, though it wouldn't be hard to contrive its use to solve._