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2011 OIM Problems/Problem 2

Revision as of 15:51, 14 December 2023 by Tomasdiaz (talk | contribs) (Created page with "== Problem == 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}\fr...")
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Problem

Find all positive integers $n$ for which there are three non-zero integers $x, y, z$ such that

\[x+y+z=0,\;\frac{1}{x}+\frac{1}{y}\frac{1}{z}=\frac{1}{n}\]

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

OIM Problems and Solutions

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