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

(Istrael /. Math. 9, 1971 43—48) proved that there are positive constants cand c'such that — <logloglog/í + c p\( 2"-l) P for distinct prime divisors and ]T -y<C*-l0gl0g« dl2"-l) " for the distinct positive divisors of the terms. Erdős note that similar results hold for the divisors of the numbers Q" 1 (Q is a positive integer)

, but he asked that the constants c and c' in this case depend on Q or not In [14] with P. Kiss we extended these results for Lucas numbers, futhermore we give their improvments by showing that the constants in the inequalities do not depend on the sequence. For Lehmer sequences we proved in [10] (Chapter 4, Theorem 4.1.) the following Theorem 1.3. ([10]) Let U = U(L,M) be the nondegenerate Lehmer sequence deßned in (1.2) . Then there are positive absolute constants c and c * which do not depend on the sequence U

, such that V —

< log log log n + c w

nP and 2]-^<c*-loglog n d\u

n d for any n> N

0, where N

0 depends only on the sequence U(L,M). 116