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25 April 2024

» arxiv » 2004.9155

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A pair of congruences concerning sums of central binomial coefficients
Guo-Shuai Mao ; Roberto Tauraso ;
Date:	20 Apr 2020
Abstract:	In this paper, we prove the following congruences: for any prime $pequiv1pmod3$: $$sum_{k=1}^{lfloorfrac{2p}3 floor}inom{2k}{k}(-2)^kequiv0pmod{p^2}qquad ext{ and }qquad sum_{k=0}^{lfloorfrac{5p}6 floor}frac{inom{2k}k}{(-32)^k}equivleft(frac2p ight)pmod{p^2}$$ where $left(frac{cdot}{p} ight)$ stands for the Legendre symbol.
Source:	arXiv, 2004.9155
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