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p + q^2 = r^4 , diophantine with primes

Source: 2022 Austrian Mathematical Olympiad Junior Regional Competition , Problem 4

October 4, 2022

number theoryDiophantine equationdiophantine

Problem Statement

Determine all prime numbers

p, q

and

r

with

p + q^2 = r^4

.
(Karl Czakler)