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infinitly natural solution

Source: Kosovo IMO TST 2012 problem 5

April 22, 2012
number theorygreatest common divisornumber theory proposed

Problem Statement

Prove that the equation 4n=1x+1y+1z\frac{4}{n}=\frac{1}{x}+\frac{1}{y}+\frac{1}{z} has infinitly many natural solutions
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