scholarly journals BOUNDS OF MULTIPLICATIVE CHARACTER SUMS WITH FERMAT QUOTIENTS OF PRIMES

2011 ◽  
Vol 83 (3) ◽  
pp. 456-462 ◽  
Author(s):  
IGOR E. SHPARLINSKI
Keyword(s):  
Character Sums ◽  
Multiplicative Character ◽  
Fermat Quotients ◽  
Fermat Quotient ◽  
Image Position ◽  
Multiplicative Character Sums

AbstractGiven a prime p, the Fermat quotient qp(u) of u with gcd (u,p)=1 is defined by the conditions We derive a new bound on multiplicative character sums with Fermat quotients qp(ℓ) at prime arguments ℓ.

scholarly journals Congruences involving the Fermat quotient

2013 ◽  
Vol 63 (4) ◽  
pp. 949-968
Author(s):  
Romeo Meštrović
Keyword(s):  
Fermat Quotient

scholarly journals Fermat quotient of cyclotomic units

1996 ◽  
Vol 76 (4) ◽  
pp. 335-358 ◽  
Author(s):  
Tsutomu Shimada
Keyword(s):  
Fermat Quotient ◽  
Cyclotomic Units

Almost perfect sequence pairs derived from Fermat quotient

2019 ◽  
Vol 55 (10) ◽  
pp. 599-601
Author(s):  
Lianfei Luo ◽  
Wenping Ma
Keyword(s):  
Fermat Quotient ◽  
Perfect Sequence

A note on some relations among special sums of reciprocals modulo p

2008 ◽  
Vol 58 (1) ◽  
Author(s):  
Ladislav Skula
Keyword(s):  
Linear Relation ◽  
Fibonacci Numbers ◽  
Linear Relations ◽  
Fermat Quotient ◽  
Modulo P ◽  
Mod P

AbstractIn this note the sums s(k, N) of reciprocals $$\sum\limits_{\tfrac{{kp}}{N} < x < \tfrac{{(k + 1)p}}{N}} {\tfrac{1}{x}(mod p)} $$ are investigated, where p is an odd prime, N, k are integers, p does not divide N, N ≥ 1 and 0 ≤ k ≤ N − 1. Some linear relations for these sums are derived using “logarithmic property” and Lerch’s Theorem on the Fermat quotient. Particularly in case N = 10 another linear relation is shown by means of Williams’ congruences for the Fibonacci numbers.

K2 of a Fermat quotient and the value of its L-function

K-Theory ◽  
1996 ◽  
Vol 10 (1) ◽  
pp. 73-82 ◽  
Author(s):  
Ken-Ichiro Kimura
Keyword(s):  
Fermat Quotient

scholarly journals Torsion points on the jacobian of a Fermat quotient

2009 ◽  
Vol 213 (7) ◽  
pp. 1489-1500
Author(s):  
R. Clement Fernández ◽  
J.M. Echarri Hernández ◽  
E.J. Gómez Ayala
Keyword(s):  
Torsion Points ◽  
Fermat Quotient
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