MathDB

N5

Part of 2013 Balkan MO Shortlist

Problems(1)

p^{q-1}- q^{p-1}=4n^2 diophantine without solution for primes p \ne q

Source: Balkan MO Shortlist 2013 N5 BMO

3/9/2020
Prove that there do not exist distinct prime numbers pp and qq and a positive integer nn satisfying the equation pq−1−qp−1=4n2p^{q-1}- q^{p-1}=4n^2
number theoryDiophantine equationdiophantineprimes