episciences.org_1356_1653623846
1653623846
episciences.org
raphael.tournoy+crossrefapi@ccsd.cnrs.fr
episciences.org
HardyRamanujan Journal
28047370
10.46298/journals/hrj
https://hrj.episciences.org
01
01
2014
Volume 38  2015
On congruences for certain sums of E. Lehmer's type
Shigeru
Kanemitsu
Takako
Kuzumaki
Jerzy
Urbanowicz
Let n > 1 be an odd natural number and let r (1 < r < n) be a natural number relatively prime to n. Denote by χn the principal character modulo n. In Section 3 we prove some new congruences for the sums T r,k (n) = n r ] i=1 (χn(i) i k) (mod n s+1) for s ∈ {0, 1, 2}, for all divisors r of 24 and for some natural numbers k.We obtain 82 new congruences for T r,k (n), which generalize those obtained in [Ler05], [Leh38] and [Sun08] if n = p is an odd prime. Section 4 is an appendix by the second and third named authors. It contains some new congruences for the sums Ur(n) = n
01
01
2014
1356
https://hal.archivesouvertes.fr/hal01254038v1
10.46298/hrj.2014.1356
https://hrj.episciences.org/1356

https://hrj.episciences.org/1356/pdf