1b

Part of 2022 Abelkonkurransen Finale

Problems(1)

Solve n*5^{n-n/p} = p! (p^2+1) + n for prime p and natural n

Source: 2022 Abelkonkurransen Finale, Problem 1b

Find all primes

p

and positive integers

n

n \cdot 5^{n-n/p} = p! (p^2+1) + n.

number theoryDiophantine Equations