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p/q+(p+1)/(q+1) is integer (VI Soros Olympiad 1990-00 R1 10.3)

Source:

May 28, 2024
number theory

Problem Statement

Find all pairs of prime natural numbers (p,q)(p, q) for which the value of the expression pq+p+1q+1\frac{p}{q}+\frac{p+1}{q+1} is an integer.
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