1985 USAMO Problems/Problem 1

Problem

Determine whether or not there are any positive integral solutions of the simultaneous equations \[x_1^2+x_2^2+\cdots+x_{1985}^2=y^3, \hspace{20pt} x_1^3+x_2^3+\cdots+x_{1985}^3=z^2\] with distinct integers $x_1,x_2,\cdots,x_{1985}$.

Solution

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See Also

1985 USAMO (ProblemsResources)
Preceded by
First
Problem
Followed by
Problem 2
1 2 3 4 5
All USAMO Problems and Solutions

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