Find all pairs of prime numbers $(p, q)$ for which $7pq^2 + p = q^3 + 43p^3 + 1$
Source: Dutch NMO 2015 p4
Tags: number theory, prime, Diophantine equation, diophantine
Find all pairs of prime numbers $(p, q)$ for which $7pq^2 + p = q^3 + 43p^3 + 1$