Difference between revisions of "1985 USAMO Problems/Problem 1"
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Determine whether or not there are any positive integral solutions of the simultaneous equations | Determine whether or not there are any positive integral solutions of the simultaneous equations | ||
| − | <cmath>x_1^2+x_2^2+\cdots+x_{1985}^2=y^3, | + | <cmath> |
| − | \ | + | \begin{align*} |
| − | x_1^3+x_2^3+\cdots+x_{1985}^3=z^2</cmath> | + | 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*} | ||
| + | </cmath> | ||
with distinct integers <math>x_1,x_2,\cdots,x_{1985}</math>. | with distinct integers <math>x_1,x_2,\cdots,x_{1985}</math>. | ||
Revision as of 21:12, 8 August 2021
Problem
Determine whether or not there are any positive integral solutions of the simultaneous equations
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. 
