Congruences involving Franel and Catalan-Larcombe-French numbers
| Autor: | Sun, Zhi-Hong |
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| Rok vydání: | 2015 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $\{f_n\}$ be the Franel numbers given by $f_n=\sum_{k=0}^n\binom nk^3$, and let $p>5$ be a prime. In this paper we mainly determine $\sum_{k=0}^{p-1} \binom{2k}k\frac{f_k}{m^k}\pmod p$ for $m=5,-16,16,32,-49,50,96$. Let $S_n=\sum_{k=0}^n\binom nk\binom{2k}k\binom{2n-2k}{n-k}$. We also determine $\sum_{k=0}^{p-1} \binom{2k}k\frac{S_k}{m^k}\pmod p$ for $m=7,16,25,32,64,160,800,1600, 156832$. Comment: 25 pages |
| Databáze: | arXiv |
| Externí odkaz: |
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