MathDB
Subset Y, |Y| = 2007 and mod(a - b + c - d + e, 47) <> 0

Source: IMO Shortlist 2007, N3, AIMO 2008, TST 2, P3

July 13, 2008
modular arithmeticnumber theoryDivisibilityExtremal combinatoricsAdditive combinatoricsIMO Shortlist

Problem Statement

Let X X be a set of 10,000 integers, none of them is divisible by 47. Prove that there exists a 2007-element subset Y Y of X X such that a \minus{} b \plus{} c \minus{} d \plus{} e is not divisible by 47 for any a,b,c,d,e∈Y. a,b,c,d,e \in Y. Author: Gerhard Wöginger, Netherlands
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