Here is my equation: $$97y-299x=10$$ I tried to solve like this: $$-299 =-3\cdot97-8$$ $$97=-12\cdot-8+1$$ $$-8=-8\cdot1+0$$ I'm not sure if I am correct or can I ignore the negative signs?
2026-03-25 20:35:49.1774470949
Linear diophantine equation $97y-299x=10$
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Ignore the signs.
$97 = 12\cdot8 + 1$ and $299 - 3\cdot97 = 8$ implies
$97 = 12\cdot(299 - 3\cdot97) + 1$ implies
$-12\cdot299+36\cdot97 + 97 = 1$ implies
$-12\cdot299+37\cdot97 = 1$
Multiply both sides by 10 and you get
$-120(299)+370(97) = 10$
$370(97)-120(299) = 10$
The general solution would be
$(x,y) = (120 + 97t, 370+299t)$