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Expression of primes is a square

Source: 2007 Bulgarian Autumn Math Competition, Problem 8.3

March 17, 2022
primessquarenumber theoryprime numbers

Problem Statement

Determine all triplets of prime numbers p<q<rp<q<r, such that p+q=rp+q=r and (r−p)(q−p)−27p(r-p)(q-p)-27p is a square.
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