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Nice result of divisibility

Source: Balkan MO 2006, Problem 3 - own

April 29, 2006
number theory proposednumber theory

Problem Statement

Find all triplets of positive rational numbers (m,n,p)(m,n,p) such that the numbers m+1npm+\frac 1{np}, n+1pmn+\frac 1{pm}, p+1mnp+\frac 1{mn} are integers. Valentin Vornicu, Romania
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