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Problem 1339

AIME late

Number theory Difficulty 5.1 Prove it United States competition problems · United States

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

This one wants a proof. Work it on paper, then read the official solution and mark yourself. Be honest about it: the record is only any use to you if it is.

Official solution

Solution: $.5!=120$ .

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