## 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.

### MSC:

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

### Keywords:

Bernoulli polynomial; denominator

OEIS
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### References:

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