Gauss's method of exclusions?

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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 ?