Distribution of special sequences modulo a large prime
نویسندگان
چکیده
منابع مشابه
Distribution of Special Sequences modulo a Large Prime
As it was indicated in [5], A. Odlyzko asks for which values of N the set A contains all residue classes (modp). The conjecture is that one can take N to be as small as p1/2+ε, for any positive ε and p > c with some c = c(ε). From the result of Rudnick and Zaharescu [4] it follows that in Odlyzko’s problem one can take N = c0p logp for some absolute constant c0. One of the main results of [5] i...
متن کاملGeneralized Fibonacci Sequences modulo Powers of a Prime
Let us begin by defining a generalized Fibonacci sequence (gn) with all gn in some abelian group as a sequence that satisfies the recurrence gn = gn−1 + gn−2 as n ranges over Z. The Fibonacci sequence (Fn) is the generalized Fibonacci sequence with integer values defined by F0 = 0 and F1 = 1. Recall also the Binet formula: for any integer n, Fn = (α − β)/ √ 5, where α = (1 + √ 5)/2 and β = (1− ...
متن کاملPeriod Multiplying Operators on Integer Sequences Modulo A Prime
We study properties of operators defined on the space E+(p) of right half-infinite sequences with entries chosen from Zp where p is prime. The operators in question allow solution of the problem of finding predecessor states for certain cellular automata evolutions and they can be thought of as discrete integration with respect to sequence index. These operators are self-accumulating, not solip...
متن کاملOrders Modulo A Prime
In this article I develop the notion of the order of an element modulo n, and use it to prove the famous n 2 + 1 lemma as well as a generalization to arbitrary cyclotomic polynomials. References used in preparing this article are included in the last page. §1 Introduction I might as well state one of the main results of this article up front, so the following discussion seems a little more moti...
متن کاملSubset Sums modulo a Prime
Let Zp be the finite field of prime order p and A be a subset of Zp. We prove several sharp results about the following two basic questions: (1) When can one represent zero as a sum of distinct elements of A ? (2) When can one represent every element of Zp as a sum of distinct elements of A ?
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2003
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171203206074