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

(13) H \

L

H^~

M

HN-2

ÍOR 0 (

M°

D

2) " I H

N_,-MH

N_

2 for »= 0 (mod 2) * We shall denote it by H = H{H

Q,H

},L,M) = {#Xo> and so //(0,1, L, M) is the Lehmer sequence f/(L, M)

. It was shown in [18] that in the case when L-A

2 and M - B terms of sequence G defined in (1.1) are also terms of sequence H giving in (1.3) up to possible multiplication by an integer factor. Thus the sequences H are much more general sequences than the sequences G. Some authors have studied the lower and upper bound for the terms of the sequence G which is given in (1.1) with integer constants G

0,G

},A and B. Let y and ő be the roots of the equation X

2-AX+B- 0 with condition \y\> |<5|. For example, K. Mahler (J. Math. Sei. 1,1966, 12—17) proved that if D = A

2 -4B <0 and S is a positive constant, then there is an effectively computable constant w

0 depending only on s such that |G„|> \yf~

e)

n for n>n

{ From a result of T. N. Shorey and C. L. Stewart (Math. Scand. 52,1983,24—36) it follows that |GJ> lyT'*for n>C

2y where C

p C

2 are positive numbers which are effectively computable in terms of G

0

, G,

, A and B. For the above constants P. Kiss (Math

. Sem. Notes (Kobe Univ.) 113