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

7,1979,145—152) gave the explicit values, proving that G

N * 0 for n >n

x, where - maxi

2

51

0(logj8i?|)

2

5

,4(log|G

01 + log4\D\

]'

2

)/log

2j

, furthermore if D < 0 and n > n

x, then ^ Iv\

n-n

C

i < \G\< 2^ Irl" 2|Z)|

5/2 1 J= \D\

v'

m where c - G

x - G

0y and C

3 =2e200

4

0 log|8£|(l + log log|8i?|) log] 1 6B\(G

Q

2 +G

2). In [18] we extended the results mentioned above to sequences H(H

Q,H

X,L,M), giving necessary and sufficient conditions for sequences H which have zero terms, furthermore giving lower and upper bounds for the terms. By using some results of M. Waldschmidt (Acta Arith. 37, 1979, 257—283) and C. L. Stewart (Transcendence Theory, New York, 1977) on linear forms in logarithms of algebraic numbers, we proved Theorem 1.1. ([18], Theorem 2) Let H = H(H

Q,H

X,L,M) be a generalized Lehmer sequence which is defined in (1.3). Letd=(L,M) and K = L-4M. If LK> 0, then H

n* 0 for n > max [13, min (1^1+1,1^1+2)]. If LK < 0, then H

N*0 forn >max (N

X,N

2), where N

X = min [2

6

7 log|4M|,e

39

8 ] and 114