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On multiple zeros of Bernoulli polynomials. (English) Zbl 1167.11009
The nth Bernoulli polynomial is a monic polynomial of degree n with rational coefficients. These polynomials arise in many branches of mathematics. The author proves that Bernoulli polynomials have no multiple zeros. This interesting result extends prior work of Brillhart, who obtained this conclusion for Bernoulli polynomials of odd index.
MSC:
11B68Bernoulli and Euler numbers and polynomials
12D10Algebraic theorems of location of zeros of polynomials over R or C