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\frac{a}{b} + \frac{a+1}{b+1} not an integer

Source: Dutch IMO TST1 2012 p3

January 10, 2020

number theoryInteger

Problem Statement

Determine all positive integers that cannot be written as

\frac{a}{b} + \frac{a+1}{b+1}

where

a

and

b

are positive integers.