Lucas Pseudoprimes
نویسندگان
چکیده
منابع مشابه
The Distribution of Lucas and Elliptic Pseudoprimes
Let ¿?(x) denote the counting function for Lucas pseudoprimes, and 2?(x) denote the elliptic pseudoprime counting function. We prove that, for large x , 5?(x) < xL(x)~l/2 and W(x) < xL(x)~l/3 , where L(x) = exp(logxlogloglogx/log logx).
متن کاملThe Rabin-Monier theorem for Lucas pseudoprimes
We give bounds on the number of pairs (P,Q) with 0 ≤ P,Q < n such that a composite number n is a strong Lucas pseudoprime with respect to the parameters (P,Q).
متن کاملOn the Infinitude of Lucas Pseudoprimes
It is well-known that properties (1) and (2) are satisfied if n is prime. If (1) is satisfied for some composite n, then n is called a Fibonacci pseudoprime (or FPP). If (2) is satisfied for some composite n, then n is called a Lucas pseudoprime (or LPP). Let U and V denote the sets of FPP's and LPP's, respectively. It must be remarked that, the above terminology is different from that used by ...
متن کاملOn Pseudoprimes Related to Generalized Lucas Sequences
In this paper we consider the general sequences U„ and Vn satisfying the recurrences Un+2=mUn+l + Un, Vn+2=mV„+l+V„, (1.1) where m is a given positive integer, and UQ = 0, Ux = 1, V0 = 2, V1 = m. We shall occasionally refer to these sequences as U(m) and V(m) to emphasize their dependence on the parameter m. They can be represented by the Binet forms Un = {a-ni{a-P\ Vn = a+f3\ (1.2) where a+j3 ...
متن کاملOn the Distributions of Pseudoprimes, Carmichael Numbers, and Strong Pseudoprimes
Building upon the work of Carl Pomerance and others, the central purpose of this discourse is to discuss the distribution of base-2 pseudoprimes, as well as improve upon Pomerance's conjecture regarding the Carmichael number counting function [8]. All conjectured formulas apply to any base b ≥ 2 for x ≥ x0(b). A table of base-2 pseudoprime, 2-strong pseudoprime, and Carmichael number counts up ...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1980
ISSN: 0025-5718
DOI: 10.2307/2006406