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find odd primes p,q such that x^p + y^q = pq has >=1 solution

Source: 2014 Swedish Mathematical Competition p6

April 30, 2021

number theorydiophantineDiophantine equation

Problem Statement

Determine all odd primes

p

and

q

such that the equation

x^p + y^q = pq

at least one solution

(x, y)

where

x

and

y

are positive integers.