On 2-adic Orders of Some Binomial Sums


We prove that for any nonnegative integers n and r the binomial sum n ∑ k=−n ( 2n n− k ) k is divisible by 22n−min{α(n),α(r)}, where α(n) denotes the number of 1s in the binary expansion of n. This confirms a recent conjecture of Guo and Zeng [J. Number Theory, 130(2010), 172–186]. In 1976 Shapiro [3] introduced the Catalan triangle ( k n ( 2n n−k ) )n>k>1… (More)


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@inproceedings{Pan2009On2O, title={On 2-adic Orders of Some Binomial Sums}, author={Hao Pan and Zhi-Wei Sun}, year={2009} }