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I read about quadratic diophantine equations like the Sum of 2 squares , pell equations etc.

Most methods are , or use ideas of , the chakravala , continued fractions , factoring , gcd , quadratic reciproxity , infinite descent or ring extensions.

But I read about an apparantly different method ?

Gauss apparantly used his " method of exclusions " ?

What is that ?

mick
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    I am not sure, but I think it has to do with quadratic-nonresidues ruling out specified congruences. – Peter Dec 13 '17 at 21:16
  • So a kind of sieve ?? – mick Dec 13 '17 at 21:19
  • Yes, I think, it actually is like sieving. But to be sure, do you know an example where Gauss used this method ? – Peter Dec 13 '17 at 21:22
  • Gauss used the algebraic approach. He did not use the methods of algebraic geometry. In modern mathematics it is not considered fashionable. Its use is not encouraged. Who uses these methods - they are seen as heretics. So who wants to work in mathematics - it is better to be in line with fashion trends. Although other ideas can give such a formula... https://math.stackexchange.com/questions/1513733/solving-a-diophantine-equation-of-the-form-x2-ay2-byz-cz2-with-the-co/1514030#1514030 – individ Dec 14 '17 at 04:37
  • Plz Explain further individ. For instance What is meant by " the methods of algebraic geometry " or " algebraic approach ". Parametrization ?? – mick Dec 23 '17 at 12:03

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