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Part of 2021 Centroamerican and Caribbean Math Olympiad

Problems(1)

Parcera triples

Source: 2021 Centroamerican and Caribbean Mathematical Olympiad, P1

An ordered triple

(p, q, r)

of prime numbers is called parcera if

p

q^2-4

q

r^2-4

r

p^2-4

. Find all parcera triples.

number theoryprime numbers