I need to find integer solutions for m^2 -2n^2 = 10. I've tried factoring but I couldn't find anything that worked. Does anyone have tips for problems like this?
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What have you tried? EG Did you test values of $m = 1$ to (say) 50 to find any solutions? – Calvin Lin Nov 26 '23 at 22:52
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See Pell's equation and its generalized form. – chirpyboat73 Nov 26 '23 at 22:56
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I didn't get any solutions trying small cases of m, but I tested for parity and found that m must be even. So I simplified to 2x^2 -n^2 = 10 where m=2x. – ploploploploploopy Nov 26 '23 at 23:00
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Welcome to Mathematics Stack Exchange. Did you mean $2x^2-n^2=\color{red}5$? – J. W. Tanner Nov 26 '23 at 23:07
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cf. this question – J. W. Tanner Nov 26 '23 at 23:14