Some q-Analogues of Granville and Sun’s Congruences
Abstract
In this paper, we use q-binomial theorem to establish some new q-analogues of Granville and Sun’s congruence: ∑ k=1p−1xk -k- ≡1 − xp − (x− 1)p -------p------- (mod p), and ∑ k=1p−1xk- k2 ≡1 p( p−1 ) 1+-(x-− 1)p −-xp ∑ (1−-x)k −-1 p − k k=1 (mod p), where x is a variable and p is an odd prime.
Fields of Study & Subjects
Advanced Mathematical Identities
Analytic Number Theory Research
Advanced Mathematical Theories and Applications
Publication details
- Journal / source
- Kragujevac Journal of Mathematics
- Publisher
- University Library in Kragujevac
- Volume
- 50
- Issue
- 4
- Pages
- 529–529
- Publication date
- 3 May 2026