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

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

2011-01-05

arxiv.org/abs/1101.0983v2

Mathematics

Number Theory

11 pages, to appear in Journal of Number Theory

Scientific paper

10.1016/j.jnt.2012.02.004

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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