共查询到20条相似文献,搜索用时 15 毫秒
1.
Sandro Mattarei 《Journal of Number Theory》2006,117(2):471-481
We prove that if the signed binomial coefficient viewed modulo p is a periodic function of i with period h in the range 0?i?k, then k+1 is a power of p, provided h is not too large compared to k. (In particular, 2h?k suffices). As an application, we prove that if G and H are multiplicative subgroups of a finite field, with H<G, and such that 1-α∈G for all α∈G?H, then G∪{0} is a subfield. 相似文献
2.
Zhi-Wei Sun 《Journal of Number Theory》2011,131(11):2219-2238
It is known that
3.
Let q>1 and m>0 be relatively prime integers. We find an explicit period νm(q) such that for any integers n>0 and r we have
4.
Zhi-Wei Sun 《Discrete Mathematics》2008,308(18):4231-4245
In this paper we study recurrences concerning the combinatorial sum and the alternate sum , where m>0, n?0 and r are integers. For example, we show that if n?m-1 then
5.
In this paper we establish a q-analogue of a congruence of Sun concerning the products of binomial coefficients modulo the square of a prime. 相似文献
6.
Paul Shaman 《Journal of multivariate analysis》2010,101(5):1263-1273
For a discrete time second-order stationary process, the Levinson-Durbin recursion is used to determine the coefficients of the best linear predictor of the observation at time k+1, given k previous observations, best in the sense of minimizing the mean square error. The coefficients determined by the recursion define a Levinson-Durbin sequence. We also define a generalized Levinson-Durbin sequence and note that binomial coefficients form a special case of a generalized Levinson-Durbin sequence. All generalized Levinson-Durbin sequences are shown to obey summation formulas which generalize formulas satisfied by binomial coefficients. Levinson-Durbin sequences arise in the construction of several autoregressive model coefficient estimators. The least squares autoregressive estimator does not give rise to a Levinson-Durbin sequence, but least squares fixed point processes, which yield least squares estimates of the coefficients unbiased to order 1/T, where T is the sample length, can be combined to construct a Levinson-Durbin sequence. By contrast, analogous fixed point processes arising from the Yule-Walker estimator do not combine to construct a Levinson-Durbin sequence, although the Yule-Walker estimator itself does determine a Levinson-Durbin sequence. The least squares and Yule-Walker fixed point processes are further studied when the mean of the process is a polynomial time trend that is estimated by least squares. 相似文献
7.
Pavel Trojovský 《Discrete Applied Mathematics》2007,155(15):2017-2024
Some new identities for the Fibonomial coefficients are derived. These identities are related to the generating function of the kth powers of the Fibonacci numbers. Proofs are based on manipulation with the generating function of the sequence of “signed Fibonomial triangle”. 相似文献
8.
Zhi-Wei Sun 《Journal of Number Theory》2005,115(2):371-380
To determine Euler numbers modulo powers of two seems to be a difficult task. In this paper we achieve this and apply the explicit congruence to give a new proof of a classical result due to M.A. Stern. 相似文献
10.
By using the Newton interpolation formula, we generalize the recent identities on the Catalan triangle obtained by Miana and Romero as well as those of Chen and Chu. We further study divisibility properties of sums of products of binomial coefficients and an odd power of a natural number. For example, we prove that for all positive integers n1,…,nm, nm+1=n1, and any nonnegative integer r, the expression
11.
Zhi-Hong Sun 《Journal of Number Theory》2003,102(1):41-89
Let p>3 be a prime, and denote the number of solutions of the congruence . In this paper, using the third-order recurring sequences we determine the values of Np(x3+a1x2+a2x+a3) and Np(x4+ax2+bx+c), and construct the solutions of the corresponding congruences, where a1,a2,a3,a,b,c are integers. 相似文献
12.
We present some variations on the Greene–Krammer?s identity which involve q-Catalan numbers. Our method reveals an intriguing analogy between these new identities and some congruences modulo a prime. 相似文献
13.
14.
Guodong Liu 《Journal of Number Theory》2008,128(12):3063-3071
In this paper, we establish some identities involving the Euler numbers, the Euler numbers of order 2 and the central factorial numbers, and give a new proof of a classical result due to M.A. Stern.
Video abstract
For a video summary of this paper, please visit http://www.youtube.com/watch?v=kdNsdTDA-FE. 相似文献15.
Jan Veit 《Aequationes Mathematicae》1995,49(1):47-56
Summary The multidimensional (partial) difference equation with periodical coefficients is transformed into an equation for a vector sequence. Integral formulae for the vector fundamental solution are developed and some results about its asymptotic properties are explained. As an example, the results are used for a simple difference equation on a hexagonal grid. 相似文献
16.
Hao Pan 《Discrete Mathematics》2006,306(16):1921-1940
By a very simple argument, we prove that if l,m,n∈{0,1,2,…} then
17.
Li-Lu Zhao 《Journal of Number Theory》2010,130(4):930-935
Let n be a positive odd integer and let p>n+1 be a prime. We mainly derive the following congruence:
18.
Conjecturally, the parity of the Mordell-Weil rank of an elliptic curve over a number field K is determined by its root number. The root number is a product of local root numbers, so the rank modulo 2 is (conjecturally) the sum over all places of K of a function of elliptic curves over local fields. This note shows that there can be no analogue for the rank modulo 3, 4 or 5, or for the rank itself. In fact, standard conjectures for elliptic curves imply that there is no analogue modulo n for any n>2, so this is purely a parity phenomenon. 相似文献
19.
Yossi Moshe 《Journal of Number Theory》2003,103(1):109-121
Let be a double sequence over a finite field satisfying a linear recurrence with constant coefficients, with at most finitely many nonzero elements on each row. Given a nonzero element g of , we show how to obtain an explicit formula for the number of g's in the first qn rows of A. We also characterize the cases when the density of 0's is 1. 相似文献
20.
We describe applications of the classical umbral calculus to bilinear generating
functions for polynomial sequences, identities for Bernoulli and related numbers, and
Kummer congruences.Dedicated to the Memory of Gian-Carlo Rota 相似文献