Hostname: page-component-77c89778f8-rkxrd Total loading time: 0 Render date: 2024-07-19T09:29:14.552Z Has data issue: false hasContentIssue false
  • English
  • Français

A Theorem of Glaisher

Published online by Cambridge University Press:  20 November 2018

Leonard Carlitz
Leonard Carlitz*
Affiliation:
Duke University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let

Then if p is a prime > 3, Glaisher [4] proved

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 5 , 1953 , pp. 306 - 316
Copyright
Copyright © Canadian Mathematical Society 1953

References

1. Carlitz, L., The coefficients of the reciprocal of a series, Duke Math. J., 8 (1941), 689–700.Google Scholar
2. Dickson, L. E., History of the theory of numbers, vol. 1 (Washington, 1919).Google Scholar
3. Glaisher, J. W. L., Congruences relating to the sums of products of the first n numbers and to other sums of products, Quarterly J. Math., 81 (1900), 1–35.Google Scholar
4. Glaisher, J. W. L. On the residues of the sums of products of the first p — 1 numbers, and their powers, to modulus p2 or p3, Quarterly J. Math., 81 (1900), 321–353.Google Scholar
5. Nielsen, N., Om Potenssummer of hele Tal, Nyt Tidsskrift for Mathematik, 4B (1893), 1–10.Google Scholar
6. Nielsen, N. Recherches sur les suites régulières et les nombres de Bernoulli et d'Euler, Annali di matematica (3), 22 (1914), 71–115.Google Scholar
7. Nielsen, N. Traité élémentaire des nombres de Bernoulli (Paris, 1923).Google Scholar
8. Nörlund, N. E., Vorlesungen ilber Differenzenrechnung (Berlin, 1924).Google Scholar