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diophantine with prime p, p^3 + m(p + 2) = m^2 + p + 1

Source: Dutch NMO 2012 p3

September 6, 2019
number theoryDiophantine equationdiophantine

Problem Statement

Determine all pairs (p,m)(p,m) consisting of a prime number pp and a positive integer mm, for which p3+m(p+2)=m2+p+1p^3 + m(p + 2) = m^2 + p + 1 holds.
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