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Solve p^3+q^3+1=p^2q^2 in prime numbers

Source: Cyprus 2022 Junior TST-2 Problem 2

February 21, 2022
number theoryprimesprime numbers

Problem Statement

Determine all pairs of prime numbers (p,q)(p, q) which satisfy the equation p3+q3+1=p2q2 p^3+q^3+1=p^2q^2