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arXiv · 1101.0983

Proof of some conjectures of Z.-W. Sun on congruences for Apery polynomials

Victor J. W. Guo·Jiang Zeng
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Abstract

The Apery polynomials are defined by $A_n(x)=\sum_{k=0}^{n}{n\choose k}^2{n+k\choose k}^2 x^k$ for all nonnegative integers $n$. We confirm several conjectures of Z.-W. Sun on the congruences for the sum $\sum_{k=0}^{n-1}(-1)^k(2k+1) A_k(x)$ with $x\in Z$.

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Victor J. W. Guo, Jiang Zeng. 2012-04-01. Proof of some conjectures of Z.-W. Sun on congruences for Apery polynomials. https://doi.org/10.1016/j.jnt.2012.02.004

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