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4q - 1 is prime and (p + q)/(p + r)= r - p, diophantine in primes

Source: 2022 Austrian Federal Competition For Advanced Students, Part 1 p4

October 4, 2022
prime numbersnumber theoryDiophantine equationdiophantine

Problem Statement

Find all triples (p,q,r)(p, q, r) of prime numbers for which 4q−14q - 1 is a prime number and p+qp+r=r−p\frac{p + q}{p + r} = r - p holds.
(Walther Janous)
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