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Parcera triples

Source: 2021 Centroamerican and Caribbean Mathematical Olympiad, P1

August 11, 2021
number theoryprime numbers

Problem Statement

An ordered triple (p,q,r)(p, q, r) of prime numbers is called parcera if pp divides q2−4q^2-4, qq divides r2−4r^2-4 and rr divides p2−4p^2-4. Find all parcera triples.
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