1985 USAMO Problems/Problem 1


Determine whether or not there are any positive integral solutions of the simultaneous equations \begin{align*} x_1^2 +x_2^2 +\cdots +x_{1985}^2 & = y^3,\\ x_1^3 +x_2^3 +\cdots +x_{1985}^3 & = z^2 \end{align*} with distinct integers $x_1,x_2,\cdots,x_{1985}$.


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See Also

1985 USAMO (ProblemsResources)
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Followed by
Problem 2
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All USAMO Problems and Solutions

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