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Article Dans Une Revue Hardy-Ramanujan Journal Année : 2014

On congruences for certain sums of E. Lehmer's type

Résumé

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
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Dates et versions

hal-01254038 , version 1 (11-01-2016)

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Shigeru Kanemitsu, Takako Kuzumaki, Jerzy Urbanowicz. On congruences for certain sums of E. Lehmer's type. Hardy-Ramanujan Journal, 2014, Volume 38 - 2015, ⟨10.46298/hrj.2014.1356⟩. ⟨hal-01254038⟩
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