1985 USAMO Problems/Problem 1

Problem

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 $x_1,x_2,\cdots,x_{1985}$ .

Solution

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1985 USAMO (Problems • Resources)
Preceded by First Problem	Followed by Problem 2
1 • 2 • 3 • 4 • 5
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1985 USAMO Problems/Problem 1

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