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Naughty consecutive integers - a^b+b

Source: Germany VAIMO 2015 - #2

July 11, 2015
Integerpositiveconsecutiveformnumber theory

Problem Statement

A positive integer nn is called naughty if it can be written in the form n=ab+bn=a^b+b with integers a,b≥2a,b \geq 2. Is there a sequence of 102102 consecutive positive integers such that exactly 100100 of those numbers are naughty?
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