2011 OIM Problems/Problem 2: Difference between revisions
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Find all positive integers <math>n</math> for which there are three non-zero integers <math>x, y, z</math> such that | Find all positive integers <math>n</math> for which there are three non-zero integers <math>x, y, z</math> such that | ||
<cmath>x+y+z=0,\;\frac{1}{x}+\frac{1}{y}\frac{1}{z}=\frac{1}{n}</cmath> | <cmath>x+y+z=0,\;\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{1}{n}</cmath> | ||
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ||
Latest revision as of 14:51, 14 December 2023
Problem
Find all positive integers 
for which there are three non-zero integers 
such that
![\[x+y+z=0,\;\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{1}{n}\]](http://latex.artofproblemsolving.com/b/3/a/b3a6380d645d9bd57f0122b6c16364e0ea39127c.png)
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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