Topic
Fermat quotient
About: Fermat quotient is a research topic. Over the lifetime, 93 publications have been published within this topic receiving 1260 citations.
Papers published on a yearly basis
Papers
TL;DR: Kummer's congruences are generalized by determining B k(p−1)+b (x)/(k(p)+b) ( mod p n ) , where p is an odd prime, x is a p-integral rational number and p−1∤b is the least positive solution of the congruence.
188 citations
TL;DR: In this article, analogues of Fermat quotients for a composite modulusm⩾2 are investigated, with special emphasis on various congruences. And the Wieferich numbers with basea are completely characterized in terms of the Fermat numbers.
56 citations
50 citations
TL;DR: The trace representations of two families of binary sequences derived from the Fermat quotients modulo an odd prime p are described by determining the defining pairs of all binary characteristic sequences of cosets, which coincide with the sets of pre-images modulo p2 of each fixed value of FerMat quotients.
Abstract: We describe the trace representations of two families of binary sequences derived from the Fermat quotients modulo an odd prime p (one is the binary threshold sequences and the other is the Legendre Fermat quotient sequences) by determining the defining pairs of all binary characteristic sequences of cosets, which coincide with the sets of pre-images modulo p
2 of each fixed value of Fermat quotients. From the defining pairs, we can obtain an earlier result of linear complexity for the binary threshold sequences and a new result of linear complexity for the Legendre Fermat quotient sequences under the assumption of 2
p−1 ≢ 1 mod p
2.
48 citations
TL;DR: In this paper, the q-analogues of two congruences of Morley and Granville are given, i.e., the qanalogue of a classical congruence of Lehmer.
Abstract: We establish the q-analogue of a classical congruence of Lehmer. Also, the q-analogues of two congruences of Morley and Granville are given.
35 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 5 |
| 2020 | 3 |
| 2019 | 4 |
| 2017 | 1 |
| 2016 | 4 |
| 2015 | 9 |