Difference between revisions of "1985 USAMO Problems/Problem 1"
(Created page with "==Problem== 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, \hspace{20pt} x_1^3+x_...") |
m (→See Also) |
||
| Line 12: | Line 12: | ||
==See Also== | ==See Also== | ||
| − | {{USAMO box|year= | + | {{USAMO box|year=1985|before=First<br>Problem|num-a=2}} |
{{MAA Notice}} | {{MAA Notice}} | ||
[[Category:Olympiad Number Theory Problems]] | [[Category:Olympiad Number Theory Problems]] | ||
Revision as of 11:45, 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
This problem needs a solution. If you have a solution for it, please help us out by adding it.
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. 
