Az Eszterházy Károly Tanárképző Főiskola Tudományos Közleményei. 1993. Sectio Mathematicae. (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 21)

Bui Minh Phong: Recurrence sequences and pseudoprimes

N

2 = min ^\og\dH

0\~\og\H

x\ log 2 log 2 Theorem 12. ([18], Theorem 3) Let H - H{H

q,H

x,L,M) be a generalized Lehmer sequence which is deßned in (1.3) with the condition LK< 0. Then for «> 2

5

7 log{|4A/|(#

0

2 + //,

2)}, we have M . in -C I „ I 2|űí| . 2\LK\

l

u \Kf where C

0 = 2

8

0 log|4A/|!oglog|4M|log{|4M|(//

0

2 + tf,

2)}, a = H

]- L

V

2HJ3, and a,ß are roots ofz

2 - L

]'

2 • z + M = 0. We note that in the case LK > 0 Theorem 1.2 also holds. Í.2. Prime divisors of Lehmer sequences Let R = R(A,B) be a Lucas sequence. Assume that (A,B)~ 1 and the sequence is non-degenerate, that is if y and S denote the roots of the characteristic polynomial x

2 - Ax + B = 0, then y/ Ő is not a root of unity. It is known that in this case y" -S" (1-4) y-o for any «>0. In the special case {A\B-{

3;2) the terms of sequence R are R

n = 2" -1. For this sequence P. Erdős 115