On p-Adic Approximation of Sums of Binomial Coefficients
نویسندگان
چکیده
منابع مشابه
On Sums of Binomial Coefficients
In this paper we study recurrences concerning the combinatorial sum [n r ] m = ∑ k≡r (mod m) (n k ) and the alternate sum ∑ k≡r (mod m)(−1) (n k ) , where m > 0, n > 0 and r are integers. For example, we show that if n > m−1 then b(m−1)/2c ∑ i=0 (−1) (m− 1− i i )[n− 2i r − i ]
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Let k > 1 be an integer and let p be a prime. We show that if pa k < 2pa or k = paq + 1 (with q < p/2) for some a = 1, 2, 3, . . ., then the set { (n k ) : n = 0, 1, 2, . . .} is dense in the ring Zp of p-adic integers; i.e., it contains a complete system of residues modulo any power of p.
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ژورنال
عنوان ژورنال: Journal of Mathematical Sciences
سال: 2018
ISSN: 1072-3374,1573-8795
DOI: 10.1007/s10958-018-3948-0