Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4595476 | Journal of Number Theory | 2008 | 25 Pages |
Abstract
For any positive integer n, let . Wolstenholme proved that if p is a prime ⩾5, then . The converse of Wolstenholme's theorem, which has been conjectured to be true, remains an open problem. In this article, we establish several relations and congruences satisfied by the numbers wn, and we deduce that this converse holds for many infinite families of composite integers n. In passing, we obtain a number of congruences satisfied by certain classes of binomial coefficients, and involving the Bernoulli numbers.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory