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If x-y=2,3 or 5 then f(x) is not equal to f(y)

Source: Romanian TST 2002

February 5, 2011
functionmodular arithmeticcombinatorics proposedcombinatorics

Problem Statement

Let f:Z→{1,2,…,n}f:\mathbb{Z}\rightarrow\{ 1,2,\ldots ,n\} be a function such that f(x)≠f(y)f(x)\not= f(y), for all x,y∈Zx,y\in\mathbb{Z} such that ∣x−y∣∈{2,3,5}|x-y|\in\{2,3,5\}. Prove that n≥4n\ge 4.
Ioan Tomescu
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