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Congruences involving Franel and Catalan-Larcombe-French numbers | Zhi-Hong Sun
; | Date: |
9 Feb 2015 | Abstract: | Let ${f_n}$ be the Franel numbers given by $f_n=sum_{k=0}^ninom nk^3$,
and let $p>5$ be a prime. In this paper we mainly determine $sum_{k=0}^{p-1}
inom{2k}kfrac{f_k}{m^k}pmod p$ for $m=5,-16,16,32,-49,50,96$.
Let $S_n=sum_{k=0}^ninom nkinom{2k}kinom{2n-2k}{n-k}$. We also
determine $sum_{k=0}^{p-1} inom{2k}kfrac{S_k}{m^k}pmod p$ for
$m=7,16,25,32,64,160,800,1600, 156832$. | Source: | arXiv, 1502.2499 | Services: | Forum | Review | PDF | Favorites |
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