The denominators of power sums of arithmetic progressions. (English) Zbl 1423.11029

The authors study the denominators of polynomials that represent the power sums of arithmetic progressions: \[ {\mathcal S}_{m,r}^n(x)=\sum_{k=0}^{x-1}(km+r)^n=r^n+(m+r)^n+\dots+((x-1)m+r)^n. \] They extend their earlier results on the case of power sum’s (when \(r=0,m=1\)). Specially, they give a simple explicit criterion for the integrality of the coefficients of these polynomials, and show further applications about the sequence of denominators of the Bernoulli polynomials.


11B25 Arithmetic progressions
11B68 Bernoulli and Euler numbers and polynomials


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