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pq/(p + q)=(m^2 + 6)/(m + 1) diophantine (HOMC 2018 Ind. p15)

Source:

January 31, 2020

Diophantine equationnumber theory

Problem Statement

Find all pairs of prime numbers

(p,q)

such that for each pair

(p,q)

, there is a positive integer m satisfying

\frac{pq}{p + q}=\frac{m^2 + 6}{m + 1}