A Q-ANALOGUE OF GRANVILLE’S CONGRUENCE

Elkhiri L., ÖMÜR N., KOPARAL S.

Integers, vol.22, 2022 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 22
  • Publication Date: 2022
  • Journal Name: Integers
  • Journal Indexes: Scopus
  • Bursa Uludag University Affiliated: Yes

Abstract

© 2022, Colgate University. All rights reserved.In this paper, we establish a q-analogue of Granville’s congruence as follows: ∑p−1 k=1 xk ≡1− xp − (x; q)p p (p − 1) (1 − q) + x [k]q [p]q 2 (mod [p]q ), for any real number x and odd prime p. Here [n]q = 1 + q + q2 + … + qn−1 and (x; q)n = (1 − x) (1 − xq) …(1 − xqn−1) .