科研之友
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摘要
In this paper we deduce some new supercongruences modulo powers of a prime p > 3. Let d is an element of {0, 1, ... (p - 1)/2}. We show that Sigma((p-1)/2)(k=0) ((2k)(k))((2k)(k+d))/8(k) equivalent to 0 (mod p) if. d equivalent to p+1/2 (mod 2), and Sigma((p-1)/2)(k=0) ((2k)(k))((2k)(k+d))/16(k) equivalent to (-1/p) + p(2) (-1)(d)/4 Ep-3(d + 1/2) (mod p(3)), where Ep-3(x) denotes the Euler polynomial of degree p - 3, and (-) stands for the Legendre symbol. The paper also contains some other results such as Sigma(p-1)(k=0) k((1+(-1/p))/2) ((6k)(3k))((3k)(k))/864(k) equivalent to 0 (mod p(2)).
- 出版日期2013-7
- 单位南京大学
