Geodesic
A proof of symmetry of the power sum polynomials using a novel Bernoulli number identity
Journal of integer sequences, Tome 20 (2017) no. 6.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The problem of finding formulas for sums of powers of natural numbers has been of interest to mathematicians for many centuries. Among these is Faulhabers well-known formula expressing the power sums as polynomials whose coefficients involve Bernoulli numbers. In this paper we give an elementary proof that the sum of $p$-th powers of the first $n$ natural numbers can be expressed as a polynomial in $n$ of degree $p + 1$. We also prove a novel identity involving Bernoulli numbers and use it to show the symmetry of this polynomial.
Classification : 11B68, 11B37
Keywords: number theory, power sum, Bernoulli number 
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     author = {Newsome, Nicholas J. and Nogin, Maria S. and Sabuwala, Adnan H.},
     title = {A proof of symmetry of the power sum polynomials using a novel {Bernoulli} number identity},
     journal = {Journal of integer sequences},
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     url = {http://geodesic.mathdoc.fr/item/JIS_2017__20_6_a6/}
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Newsome, Nicholas J.; Nogin, Maria S.; Sabuwala, Adnan H. A proof of symmetry of the power sum polynomials using a novel Bernoulli number identity. Journal of integer sequences, Tome 20 (2017) no. 6. http://geodesic.mathdoc.fr/item/JIS_2017__20_6_a6/