Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4593601 | Journal of Number Theory | 2015 | 16 Pages |
Abstract
Let PnPn denote the set of positive integers which are prime to n . Let BnBn be the n -th Bernoulli number. For any prime p>5p>5 and integer r≥2r≥2, we prove that∑l1+l2+⋯+l5=prl1,⋯,l5∈Pp1l1l2l3l4l5≡−5!6pr−1Bp−5(modpr). This gives an extension of a family of curious congruences found by the author, Cai and Zhao.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Liuquan Wang,