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Congruences concerning generalized central trinomial coefficients.
- Source :
-
Proceedings of the American Mathematical Society . Sep2022, Vol. 150 Issue 9, p3725-3738. 14p. - Publication Year :
- 2022
-
Abstract
- For any n\in \mathbb {N}=\{0,1,2,\ldots \} and b,c\in \mathbb {Z}, the generalized central trinomial coefficient T_n(b,c) denotes the coefficient of x^n in the expansion of (x^2+bx+c)^n. Let p be an odd prime. In this paper, we determine the summations \sum _{k=0}^{p-1}T_k(b,c)^2/m^k modulo p^2 for integers m with certain restrictions. As applications, we confirm some conjectural congruences of Sun [Sci. China Math. 57 (2014), pp. 1375–1400]. [ABSTRACT FROM AUTHOR]
- Subjects :
- *BINOMIAL coefficients
*INTEGERS
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 150
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 157716577
- Full Text :
- https://doi.org/10.1090/proc/15985