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- Thread starter ramsey2879
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When p is of the form 8k +-1, then X^2 ==2 Mod (p) is always the case! The theory of quadratic residues was developed by Gauss.

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Well, there is a question here: 5^2-2(2)^2 = 25-8 = 17,

But: 17 = 2(3^2)-(1)^2 = 18-1.

So you' ll have to look at that again.

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Note that for odd integers, X^2- 2Y^2 always equals 7 mod 8. Sorry for the miscommunication.ramsey2879 said:My conjecture as corrected stands

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All odd squaes are congruent to 1 Mod 8. (2x+1)^2 = 4x^2+4x+1 =

4x(x+1) +1 ==1 Mod 8.

4x(x+1) +1 ==1 Mod 8.

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