1982 USAMO Problems/Problem 2: Difference between revisions

Revision as of 05:12, 30 December 2019

Problem

Let $S_r=x^r+y^r+z^r$ with $x,y,z$ real. It is known that if $S_1=0$ ,

$(*)$ $\frac{S_{m+n}}{m+n}=\frac{S_m}{m}\frac{S_n}{n}$

for $(m,n)=(2,3),(3,2),(2,5)$ , or $(5,2)$ . Determine all other pairs of integers $(m,n)$ if any, so that $(*)$ holds for all real numbers $x,y,z$ such that $x+y+z=0$ .

Solution

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 == Problem ==
-Let <math>X_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>,
+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>

1982 USAMO (Problems • Resources)
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1982 USAMO Problems/Problem 2: Difference between revisions

Revision as of 05:12, 30 December 2019

Problem

Solution

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