Competition problem — Number theory

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Number theory Difficulty 5.1 AIME, harder Prove it United States

Problem:
Find the largest integer that divides $m^{5}-5 m^{3}+4 m$ for all $m \geq 5$ .

Solution

Solution: $.5!=120$ .

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.