BINOMIAL COEFFICIENTS AND THE RING OF p-ADIC INTEGERS
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چکیده
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.
منابع مشابه
0812 . 3089 BINOMIAL COEFFICIENTS AND THE RING OF p - ADIC INTEGERS
Let k > 1 be an integer and let p be a prime. We show that if p a k < 2p a or k = p a q + 1 (with 2q p) for some a = 1, 2, 3,. .. , then the set { ` n k ´ : n = 0, 1, 2,. .. } is dense in the ring Z p of p-adic integers, i.e., it contains a complete system of residues modulo any power of p.
متن کامل2 00 8 Preprint , arXiv : 0812 . 3089 BINOMIAL COEFFICIENTS AND THE p - ADIC INTEGRAL RING
Let k be a positive integer and p be a prime. We show that if p a k < 2p a or k = p a q + 1 (with 2q p) for some a = 0, 1, 2,. .. , then the set { ` n k ´ : n = 0, 1, 2,. .. } is dense in the ring Z p of p-adic integers, i.e., it contains a complete system of residues modulo any power of p.
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متن کاملStatement Julian
My mathematical research interests are in number theory and algebraic geometry. My thesis work concerns the arithmetic of a family of rational numbers known as multiple harmonic sums, which are truncated approximations of multiple zeta values. I explore new structures underlying relations involving multiple harmonic sums, p-adic L-values, Bernoulli numbers, and binomial coefficients. This is us...
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تاریخ انتشار 2010