哈尔滨工业大学学报（英文版）2003，Vol.10Issue(2)：183-189,7.
On the multiplicity of binary recurrences
On the multiplicity of binary recurrences
摘要
Abstract
LetA ∈ N,B ∈ Z with gcd (A,B) = 1 ,B(∈/){ - 1,0,1 }. For the binary recurrence (Lucas se-quence) of the form u0 = 0, u1 = 1 , un+2 = Aun+1 + Bun, let N1 (A,B,k) be the number of the terms n of | un= k, where k ∈ N. In this paper, using a new result of Bilu, Hanrot and Voutier on prinmitive divisors, weproved thatN1(A,B,k) ≤lexceptN1(1, -2,1) =5[n = 1,2,3,5,13], N1(1, -3,1) =3[n = 1,2,5],N1(1,-5,1) =3[n = 1,2,7],N1(1,B,1) =2(B(∈/) {-2, -3, -5})[n = 1,2], N1(12, -55,1) =2[n = 1,5], N1(12,-377,1) =2[n = 1,5], N1(A,B,1) =2(A2 +B =±1,A ＞ 1)[n = 1,3], N1(1,-2,3) = 2[n = 4,8], N1(A,B,A) = 2(A2 +2B =±1,A ＞ l[n = 2,4]. For Lehmer sequence, we gota similar result. In addition, we also obtained some applications of the above results to some Diophantime equa-tions.关键词
binary recurrences/diophantine equations/multiplicities/Lucas and Lehmer sequences/primitive divisors/cryptographic problemsKey words
binary recurrences/diophantine equations/multiplicities/Lucas and Lehmer sequences/primitive divisors/cryptographic problems分类
数理科学引用本文复制引用
董晓蕾,沈灏..On the multiplicity of binary recurrences[J].哈尔滨工业大学学报（英文版）,2003,10(2):183-189,7.基金项目
Sonsored by the Postdoctoral Science Foundation of China(2001 ) and the National Natural Science Foundation of China( Grant No. 60072018 ). （2001 ）
