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Partition such that there exists a,b,c with a^b=c

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April 23, 2011
number theory proposednumber theory

Problem Statement

Let m≥2m\ge 2 be an integer. Find the smallest positive integer n>mn>m such that for any partition with two classes of the set {m,m+1,…,n}\{ m,m+1,\ldots ,n \} at least one of these classes contains three numbers a,b,ca,b,c (not necessarily different) such that ab=ca^b=c.
Ciprian Manolescu
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