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any partition of the set {m,m + 1,..,k} into 2 classes contains ab,c such a^b=c

Source: Switzerland - Swiss TST 2002 p10

February 18, 2020

partitionSubsetsnumber theory

Problem Statement

Given an integer

m\ge 2

, find the smallest integer

k > m

such that for any partition of the set

\{m,m + 1,..,k\}

into two classes

A

and

B

at least one of the classes contains three numbers

a,b,c

(not necessarily distinct) such that

a^b = c