Huaiyin Normal University

most citedCongruences concerning Legendre polynomials

47 citations

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Zhi-Hong Sun3

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math.NT2010

Identities and congruences for a new sequence

Zhi-Hong Sun

Let $[x]$ be the greatest integer not exceeding $x$ . In the paper we introduce the sequence ${U_{n}}$ given by $U_{0} = 1$ and $U_n=-2\sum_{k=1}^{[n/2]}\binom n{2k}U_{n-2k}\quad(n\ge 1…

math.NT2010★ 47 cited

Congruences concerning Legendre polynomials

Zhi-Hong Sun

Let $p$ be an odd prime. In the paper, by using the properties of Legendre polynomials we prove some congruences for $\sum_{k = 0}^{\frac{p - 1}{2}} (k 2 k)^{2} m^{- k} mod p^{2}$ . In par…