# Diophantine equation

Algebra Level pending

Are there infinitely many distinct positive integer solutions (i.e $$a\neq b\neq c\neq x\neq y\neq z$$) to this system of equations? $a+b+c=x+y+z$ $a^{2}+b^{2}+c^{2}=x^{2}+y^{2}+z^{2}$

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