Results about generalised Pythagorean triples

Asked Jul 05 '23 at 18:55

Active Jul 05 '23 at 18:55

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I reduced a problem I am working on to the question of whether the equation $$x^2+y^2=6z^2$$ has a non-trivial integer solution.

Thus I am looking for any results about the solution space of equations of the form $$ax^2+by^2+cz^2=0$$ for $a,b,c \in \mathbb{Z}$ (or $\mathbb{R}$).

asked Jul 05 '23 at 18:55

Schief

2

Fermat's sum of two squares theorem addresses this. – lulu Jul 05 '23 at 19:11
The only solution to this is trivial. – poetasis Jul 05 '23 at 19:50
https://math.stackexchange.com/questions/27471/proof-of-legendres-theorem-on-the-ternary-quadratic-form – Will Jagy Jul 05 '23 at 21:36

Results about generalised Pythagorean triples

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