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Junior Balkan Mathematical Olympiad 2020- P4

Source: JBMO 2020

September 11, 2020

number theoryprime numbersJunior BalkanJuniorjbmo2020geometry

Problem Statement

Find all prime numbers

p

and

q

such that

1 + \frac{p^q - q^p}{p + q}

is a prime number.
Proposed by Dorlir Ahmeti, Albania