Difference between revisions of "1982 USAMO Problems/Problem 2"
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== Problem == | == Problem == | ||
| − | Let <math> | + | Let <math>S_r=x^r+y^r+z^r</math> with <math>x,y,z</math> real. It is known that if <math>S_1=0</math>, |
<math>(*) </math> <math>\frac{S_{m+n}}{m+n}=\frac{S_m}{m}\frac{S_n}{n}</math> | <math>(*) </math> <math>\frac{S_{m+n}}{m+n}=\frac{S_m}{m}\frac{S_n}{n}</math> | ||
Revision as of 05:12, 30 December 2019
Problem
Let 
with 
real. It is known that if 
,
for 
, or 
. Determine all other pairs of integers 
if any, so that holds for all real numbers such that 
.
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See Also
| 1982 USAMO (Problems • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 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. 
