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IMO ShortList 1998, number theory problem 3

Source: IMO ShortList 1998, number theory problem 3

October 22, 2004

modular arithmeticpigeonhole principlenumber theoryDivisibilityIMO Shortlistcombinatorics

Problem Statement

Determine the smallest integer

n\geq 4

for which one can choose four different numbers

a,b,c

and

d

from any

n

distinct integers such that

a+b-c-d

is divisible by

20