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RO-NMO 2013 Problem 3

    Find all injective functions f:Z→Zf:\mathbb{Z}\to \mathbb{Z} that satisfy: ∣f(x)−f(y)∣≤∣x−y∣\left| f\left( x \right)-f\left( y \right) \right|\le \left| x-y \right| ,for any x,y∈Zx,y\in \mathbb{Z} .

    Dataset text AI-MO AoPS. Quoted with source.

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