Could you please help me for this proof :
Prove that there is no triplet of integers (x, y, z) prime to each other such that: $$x²+y² = 3z²$$
I tried to make a proof by contradiction...
2026-04-24 22:11:23.1777068683
Prime numbers equation
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RHS is divisible by $3$. If either $x$ or $y$ are $1$ or $-1$ modulo $3$ then $3$ will not divide the LHS. Hence $x$ and $y$ must be both $0$ modulo $3$ which implies the GCD of $x$ and $y$ must be at least $3$. Hence they can't be coprime.