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p^2+qs, p^2 +qr perfect squares - All-Russian MO 1994 Regional (R4) 9.7

Source:

August 26, 2024

number theoryPerfect Square

Problem Statement

Find all prime numbers

p,q,r,s

such that their sum is a prime number and

p^2+qs

and

p^2 +qr

are squares of integers.