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Article overview
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Some super congruences involving binomial coefficients | Hui-Qin Cao
; Zhi-Wei Sun
; | Date: |
15 Jun 2010 | Abstract: | Let $p>3$ be a prime. We show that
$$T_{p-1}=(p/3)3^{p-1} (mod p^2},$$ where the central trinomial coefficient
$T_n$ is the constant term in the expansion of $(1+x+x^{-1})^n$. We also prove
three congruences conjectured by Sun one of which is as follows:
$$sum_{k=0}^{p-1}inom{p-1}{k}inom{2k}{k}((-1)^k-(-3)^{-k})=(p/3)(3^{p-1}-1)
(mod p^3).$$ | Source: | arXiv, 1006.3069 | Services: | Forum | Review | PDF | Favorites |
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