Difference between revisions of "1985 USAMO Problems/Problem 1"
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[[Category:Olympiad Number Theory Problems]] | [[Category:Olympiad Number Theory Problems]] | ||
Revision as of 12:45, 18 July 2016
Problem
Determine whether or not there are any positive integral solutions of the simultaneous equations
![\[x_1^2+x_2^2+\cdots+x_{1985}^2=y^3, \hspace{20pt} x_1^3+x_2^3+\cdots+x_{1985}^3=z^2\]](http://latex.artofproblemsolving.com/3/8/e/38ef2e42883b1894da821751171fb97206bcb342.png)
with distinct integers 
.
Solution
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See Also
| 1985 USAMO (Problems • Resources) | ||
| Preceded by First Problem |
Followed by Problem 2 | |
| 1 • 2 • 3 • 4 • 5 | ||
| All USAMO Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
