Say I have the equation a^2 - 10b^2 = 2. So even though this is an equation in two variables and not one, I can still reduce mod P to a^2 = 2 (mod 5) and use the fact that it has no integer solutions mod 5 to conclude the original equation has no integer solutions, correct? Also does this only work modulo a prime, or can I do this modulo any natural number?(adsbygoogle = window.adsbygoogle || []).push({});

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# Proving non-existence of integer solutions by reducing mod p

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