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find primes p<q< r so that 25pq + r = 2004 and pqr + 1 is a perfect square

Source: Mexican Mathematical Olympiad 2004 OMM P1

July 31, 2018

primesPerfect Squarenumber theory

Problem Statement

Find all the prime number

p, q

and r with

p < q < r

, such that

25pq + r = 2004

and

pqr + 1

is a perfect square.