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Polynomial extension of Fleck's congruence | | Zhi-Wei Sun
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1 Jul 2005 | | Subject: | Number Theory; Combinatorics MSC-class: 11B65; 05A10; 11A07; 11B68; 11S05 | math.NT math.CO | | Abstract: | Let p be a prime, and let f(x) be an integer-valued polynomial. By a combinatorial approach, we obtain a nontrivial lower bound of the p-adic order of the sum $$sum_{k=r(mod p^{eta})}inom{n}{k}(-1)^k f([(k-r)/p^{alpha}]),$$ where $alphageetage 0$, $nge 0$ and $rin Z$. This polynomial extension of Fleck’s congruence has various backgrounds and several consequences. | | Source: | arXiv, math.NT/0507008 | | Services: | Forum | Review | PDF | Favorites | |
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