Irregular prime divisors of the Bernoulli numbers

Author:
Wells Johnson

Journal:
Math. Comp. **28** (1974), 653-657

MSC:
Primary 10A40; Secondary 12A35, 12A50

DOI:
https://doi.org/10.1090/S0025-5718-1974-0347727-0

MathSciNet review:
0347727

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Abstract: If *p* is an irregular prime, , then the indices 2*n* for which the Bernoulli quotients are divisible by are completely characterized. In particular, it is always true that and that if *(p,2n)* is an irregular pair. As a result, we obtain another verification that the cyclotomic invariants of Iwasawa all vanish for primes .

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1974-0347727-0

Keywords:
Bernoulli numbers,
irregular primes,
cyclotomic invariants

Article copyright:
© Copyright 1974
American Mathematical Society