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On the Sum of Powers of Consecutive Integers

It is well known that the sum of cubes of three consecutive integers is always divisible by 9. Is this an isolated incident? We showed that this can be generalized to the fact that the sum of the mkth power of any k consecutive integers is always divisible by the square of k if the exponent mk is an odd integer. If m is even, the situation is more complicated: the sum of the mkth powers of k consecutive integers is divisible by the square of k for some even integers m and not divisible by the square of k for other even integers. For the case when k is an odd prime, we have a complete characterization on the integer m for which the sum of the mkth power of any k consecutive integers is divisible by the square of k.

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THE COLLEGE MATHEMATICS JOURNAL; Vol.51 No.4 September 2020

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Penerbit

: .,

Deskripsi Fisik

p. 295 - 301

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English

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Pernyataan Tanggungjawab

Chungwu Ho, Gregory Mellblom, Marc Frodyma

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