## Irregular prime divisors of the Bernoulli numbers

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- by Wells Johnson PDF
- Math. Comp.
**28**(1974), 653-657 Request permission

## Abstract:

If*p*is an irregular prime, $p < 8000$, then the indices 2

*n*for which the Bernoulli quotients ${B_{2n}}/2n$ are divisible by ${p^2}$ are completely characterized. In particular, it is always true that $2n > p$ and that ${B_{2n}}/2n\;\nequiv ({B_{2n + p - 1}}/2n + p - 1)\pmod {p^2}$ if

*(p,2n)*is an irregular pair. As a result, we obtain another verification that the cyclotomic invariants ${\mu _p}$ of Iwasawa all vanish for primes $p < 8000$.

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## Additional Information

- © Copyright 1974 American Mathematical Society
- 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