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1^n+2^n+...+15^n is divisible by 480 for each odd n >=5

Source: 1996 Estonia National Olympiad Final Round grade 11 p4

March 11, 2020
number theorydivisibledividesSum of powersSum

Problem Statement

Prove that, for each odd integer n≥5n \ge 5, the number 1n+2n+...+15n1^n+2^n+...+15^n is divisible by 480480.
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