MathDB

Integer set

Source: Chinese TST 2009 2nd quiz P2

March 21, 2009

modular arithmeticalgebrapolynomialnumber theorycombinatorics proposedcombinatoricsAdditive combinatorics

Problem Statement

Find all the pairs of integers

(a,b)

satisfying ab(a \minus{} b)\not \equal{} 0 such that there exists a subset

Z_{0}

of set of integers

Z,

for any integer

n

, exactly one among three integers n,n \plus{} a,n \plus{} b belongs to

Z_{0}