p-adic Proofs of congruences for the Bernoulli numbers |
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Authors: | Wells Johnson |
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Affiliation: | Department of Mathematics, Bowdoin College, Brunswick, Maine 04011 USA |
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Abstract: | Many of the classical theorems for the Bernoulli numbers, particularly those congruences needed in the study of irregular primes, follow easily from the existence of the (p ? 1)st roots of unity in the ring of p-adic integers. Proofs are given for the von Staudt-Clausen theorem, the theorem of J. C. Adams, the Friedmann-Tamarkine congruence, a theorem of Vandiver, special cases of the congruences of Voronoi, Kummer, and Carlitz, and the congruences of E. Lehmer. |
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