Iris F. Zhang

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We observe that the classical Faulhaber's theorem on sums of odd powers also holds for an arbitrary arithmetic progression, namely, the odd power sums of any arithmetic progression a+ b, a+ 2b,. .. , a+ nb is a polynomial in na+ n(n + 1)b/2. While this assertion can be deduced from the original Fauhalber's theorem, we give an alternative formula in terms of(More)
We introduce the notion of arithmetic progression blocks or AP-blocks of Z n , which can be represented as sequences of the form (x, x + m, x + 2m,. .. , x + (i − 1)m) (mod n). Then we consider the problem of partitioning Z n into AP-blocks for a given difference m. We show that subject to a technical condition, the number of partitions of Z n into mAP(More)
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