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Prove that the function n^{2007}-n! is injective

Source: Romanian TST 4 2007, Problem 1

May 23, 2007
functioninequalitiesfloor functionfactorialnumber theory proposednumber theory

Problem Statement

Prove that the function f:N⟶Zf : \mathbb{N}\longrightarrow \mathbb{Z} defined by f(n)=n2007−n!f(n) = n^{2007}-n!, is injective.
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