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Diophantine equation with primes

Source: Argentina IberoAmerican TST 2024 P1

August 9, 2024
number theoryDiophantine equationprime numbers

Problem Statement

Find all positive prime numbers pp, qq that satisfy the equation p(p4+p2+10q)=q(q2+3)p(p^4+p^2+10q)=q(q^2+3)