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24 divides (n^5 -5n^3 + 4n)/(n + 2)

Source: Spanish Mathematical Olympiad 1976 P4

December 23, 2022
number theorydivides

Problem Statement

Show that the expression n5−5n3+4nn+2\frac{n^5 -5n^3 + 4n}{n + 2} where n is any integer, it is always divisible by 2424.
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