منابع مشابه
On Fleck
Let p be a prime, and let n > 1 and r be integers. In this paper we study Fleck’s quotient Fp(n, r) = (−p) X
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Nowadays this result plays important roles in many aspects. Recently Sun and Wan investigated Fp(n, r) mod p in [SW2]. In this paper, using p-adic methods we determine (Fp(m, r) − Fp(n, r))/(m − n) modulo p in terms of Bernoulli numbers, where m > 0 is an integer with m 6= n and m ≡ n (mod p(p − 1)). Consequently, Fp(n, r) mod pordp(n)+1 is determined; for example, if n ≡ n∗ (mod p− 1) with 0 <...
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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 ...
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ژورنال
عنوان ژورنال: Der Hautarzt
سال: 2016
ISSN: 0017-8470,1432-1173
DOI: 10.1007/s00105-016-3780-8