1

Part of 2019 IOM

Problems(1)

Source: International Olympiad of Metropolises 2019 P1

Three prime numbers

p,q,r

and a positive integer

n

are given such that the numbers

\frac{p+n}{qr}, \frac{q+n}{rp}, \frac{r+n}{pq}

are integers. Prove that

p=q=r

.
Nazar Agakhanov

number theoryprime numbersKvant