Polynomial Extension of Fleck ’ S Congruence 3

نویسندگان

  • ZHI-WEI SUN
  • C. S. Weisman
چکیده

Let p be a prime, and let f (x) be an integer-valued polynomial. By a combinatorial approach, we obtain a nontrivial lower bound of the p-adic order of the sum k≡r (mod p β) n k (−1) k f k − r p α , where α β 0, n p α−1 and r ∈ Z. This polynomial extension of Fleck's congruence has various backgrounds and several consequences such as k≡r (mod p α) n k a k ≡ 0 mod p n−p α−1 ϕ(p α) provided that α > 1 and a ≡ −1 (mod p).

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تاریخ انتشار 2006