A sum of binomial coefficients
نویسندگان
چکیده
منابع مشابه
The Sum of Binomial Coefficients and Integer Factorization
The combinatorial sum of binomial coe cients n i r (a) := X k⌘i (mod r) ✓ n k ◆ a k has been studied widely in combinatorial number theory, especially when a = 1 and a = 1. In this paper, we connect it with integer factorization for the first time. More precisely, given a composite n, we prove that for any a coprime to n there exists a modulus r such that the combinatorial sum has a nontrivia...
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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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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1978
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1978-0502014-6