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p^2 + 5pq + 4q^2 is a perfect square.

Source: 2017 Saudi Arabia JBMO Training Tests 6

May 28, 2020
number theoryPerfect Square

Problem Statement

Find all pairs of prime numbers (p,q)(p, q) such that p2+5pq+4q2p^2 + 5pq + 4q^2 is a perfect square.