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Find a solution: $3(x^2+y^2+z^2)=10(xy+yz+zx)$

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If $n = a^2 + b^2 + c^2$ for positive integers $a$, $b$,$c$, show that there exist positive integers $x$, $y$, $z$ such that $n^2 = x^2 + y^2 + z^2$.

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How to find all rational solutions of $\ x^2 + 3y^2 = 7 $?

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Solutions to $ax^2 + by^2 = cz^2$

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Integer solutions for $\frac{1}{x^2}+\frac{1}{y^2}=\frac{1}{z^2}$?

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When is the sum of two squares the sum of two cubes

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Find a solution: $3(x^2+y^2+z^2)=10(xy+yz+zx)$

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