MathDB

Prime numbers and perfect squares

Source: Turkey JBMO Team Selection Test 2013, P2

May 31, 2013

modular arithmeticnumber theoryprime numbersnumber theory proposed

Problem Statement

a) Find all prime numbers

p, q, r

satisfying

3 \nmid p+q+r

and

p+q+r

and

pq+qr+rp+3

are both perfect squares.
b) Do there exist prime numbers

p, q, r

such that

3 \mid p+q+r

and

p+q+r

and

pq+qr+rp+3

are both perfect squares?