On 2-adic orders of some binomial sums
Pan, Hao · Sun, Zhi-Wei
Original · EN
We prove that for any nonnegative integers n and r the binomial sum ∑ₖ₌₋ₙⁿ2nn-kk²ʳ is divisible by 22n-{α(n),α(r)}, where α(n) denotes the number of 1's in the binary expansion of n. This confirms a recent conjecture of Guo and Zeng.
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