Congruences concerning Legendre polynomials III

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Sun, Zhi-Hong;
  • Subject: Mathematics - Combinatorics | 11A07, 33C45, 11E25, 11L10, 05A10 | Mathematics - Number Theory

Let $p>3$ be a prime, and let $R_p$ be the set of rational numbers whose denominator is coprime to $p$. Let $\{P_n(x)\}$ be the Legendre polynomials. In this paper we mainly show that for $m,n,t\in R_p$ with $m\not\e 0\pmod p$, $$\align &P_{[\frac p6]}(t) \e -\Big(\frac... View more
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