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

Source: 2019 Grand Duchy of Lithuania, Mathematical Contest p4 (Baltic Way TST)

October 3, 2020
number theoryPerfect Square

Problem Statement

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