# Joel's Problem 5

Number Theory Level pending

Suppose that in a set $$A$$ of mutually coprime positive integers, for any ordered triple $$(x, y, z)$$ in $$A$$ with $$x, y, z$$ mutually distinct, $$x^{2}$$ is a factor of $$y^{3}+z^{3}$$. Let $$X$$ be the number of distinct elements in $$A$$. Find the maximum possible value of $$X$$.

(If $$X<3$$, $$(x, y, z)$$ might not exist.)

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