Determine all triplets of prime numbers $p<q<r$, such that $p+q=r$ and $(r-p)(q-p)-27p$ is a square.
Problem
Source: 2007 Bulgarian Autumn Math Competition, Problem 8.3
Tags: primes, square, number theory, prime numbers
Source: 2007 Bulgarian Autumn Math Competition, Problem 8.3
Tags: primes, square, number theory, prime numbers
Determine all triplets of prime numbers $p<q<r$, such that $p+q=r$ and $(r-p)(q-p)-27p$ is a square.