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A general family of congruences for Bernoulli numbers

    https://doi.org/10.1142/S1793042118501129Cited by:1 (Source: Crossref)

    We prove a general family of congruences for Bernoulli numbers whose index is a polynomial function of a prime, modulo a power of that prime. Our family generalizes many known results, including the von Staudt–Clausen theorem and Kummer’s congruence.

    AMSC: 11B68, 11A07

    References

    • 1. H. Cohen, Number Theory. Vol. II. Analytic and Modern Tools, Graduate Texts in Mathematics, Vol. 240 (Springer, New York, 2007). Google Scholar
    • 2. Z.-H. Sun, Congruences concerning Bernoulli numbers and Bernoulli polynomials, Discrete Appl. Math. 105(1–3) (2000) 193–223. Crossref, Web of ScienceGoogle Scholar
    • 3. L. C. Washington, Introduction to Cyclotomic Fields, Graduate Texts in Mathematics, Vol. 83, 2nd edn. (Springer-Verlag, New York, 1997). CrossrefGoogle Scholar
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