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Diophantine equation with primes

Source: Centroamerican 2011, Problem 4

June 22, 2011
number theoryprime numbersnumber theory proposed

Problem Statement

Find all positive integers pp, qq, rr such that pp and qq are prime numbers and 1p+1+1q+1−1(p+1)(q+1)=1r.\frac{1}{p+1}+\frac{1}{q+1}-\frac{1}{(p+1)(q+1)} = \frac{1}{r}.
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