SMO Primes!

Number Theory Level 3

Let \(p\), \(q\) and \(r\) be prime numbers such that


What is the value of \(p^2+q^2+r^2\)?

This problem appeared in the SMO - 2014.
This problem is a part of the set "Olympiads and Contests Around the World - 2." You can see rest of the problems here.

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