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Equal primes

Source: International Olympiad of Metropolises 2019 P1

September 3, 2019
number theoryprime numbersKvant

Problem Statement

Three prime numbers p,q,rp,q,r and a positive integer nn are given such that the numbers p+nqr,q+nrp,r+npq \frac{p+n}{qr}, \frac{q+n}{rp}, \frac{r+n}{pq} are integers. Prove that p=q=rp=q=r .
Nazar Agakhanov
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