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arithmetic progressions

Source: 2011 Romania TST Problem 2

February 4, 2012
floor functionpigeonhole principlearithmetic sequenceRamsey Theorynumber theory proposednumber theory

Problem Statement

Prove that the set S={⌊nπ⌋∣n=0,1,2,3,…}S=\{\lfloor n\pi\rfloor \mid n=0,1,2,3,\ldots\} contains arithmetic progressions of any finite length, but no infinite arithmetic progressions.
Vasile Pop
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