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- W1667996953 abstract "Let p be a prime, and let n>0 and r be integers. In 1913 Fleck showed that $$F_p(n,r)=(-p)^{-[(n-1)/(p-1)]}sum_{k=r(mod p)}binom{n}{k}(-1)^kinZ.$$ Nowadays this result plays important roles in many aspects. Recently Sun and Wan investigated $F_p(n,r)$ mod p in [SW2]. In this paper, using p-adic methods we determine $(F_p(m,r)-F_p(n,r))/(m-n)$ modulo p in terms of Bernoulli numbers, where m>0 is an integer with $mnot=n$ and $m=n (mod p(p-1))$. Consequently, $F_p(n,r)$ mod $p^{ord_p(n)+1}$ is determined; for example, if $n=n_*(mod p-1)$ with $0 0$ and $lge 0$ are integers with $2le n-lle p$ then $$frac{1}{p^{n-l}}sum_{l<kle n} binom{p^a n-d}{p^a k-d}(-1)^{pk}binom{k-1}{l} =frac{(-1)^{l-1}n!}{l!(n-l)}B_{p-n+l} (mod p)$$ for all d=1,...,max{p^{a-2},1}." @default.
- W1667996953 created "2016-06-24" @default.
- W1667996953 creator A5075574908 @default.
- W1667996953 date "2006-08-14" @default.
- W1667996953 modified "2023-09-27" @default.
- W1667996953 title "FLECK QUOTIENTS AND BERNOULLI NUMBERS" @default.
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- W1667996953 hasPublicationYear "2006" @default.
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