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p^2 = q^2 + r^n , diophantine with 3 primes

Source: 2020 Austrian Regional Competition For Advanced Students p4

November 22, 2020

number theoryDiophantine equationdiophantine

Problem Statement

Find all quadruples

(p, q, r, n)

of prime numbers

p, q, r

and positive integer numbers

n

, such that

p^2 = q^2 + r^n

(Walther Janous)