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Centroamerican 2018, problem 4

Source: 2018 Centroamerican and Caribbean Math Olympiad

June 25, 2018
number theoryCentroamerican

Problem Statement

Determine all triples (p,q,r)(p, q, r) of positive integers, where p,qp, q are also primes, such that r2−5q2p2−1=2\frac{r^2-5q^2}{p^2-1}=2.
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