Az Eszterházy Károly Tanárképző Főiskola Tudományos Közleményei. 1989. 19/8. (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 19)

Csóké Lajos: Sturm tételének gyakorlati alkalmazásáról.

- 47 PÉTER KISS* AND DUI MINI! PHONG** RECIPROCAL SUM OF PRIME DIVISORS OF LUCAS NUMHF.RS ABSTARCT: In this paper, among othore, uie shou that for any non-degenerate Lxtcas sequence the reciprocal sum of the prime di vi nor it of the it

1 term in lesti than tog log log n -*- c for any n>n

Q. The constant c is an absolute one, only n depends on the parameters of the sequence. It is an extension of a result of P.

Erdős who proved it for Mersenne numbers. Let R = be a Lucas sequence of integers ^ n = o defined by R == A R * B R „ (n>l>, n n-i n - 2 * where A, B are fixed non-zero integers and the ini timl t.prms are R

o~0

, R

?=l. Throughout the paper we assume that CA,B)~1 and the sequence is non-degenerate, that, is if a and ß denote the roots of the characteristic polynomial x

?'-Ax-B, then ci/fi is not a root of unity. It is known that in this case Cl) R as n a~f) for any n£0 . Furthermore if p is a prime and pfB, then there are terms in R such that p|R . We shall denote the Research partially supported by Hungarian National Foundati oh for Sci&fti i f ic ft&s&Qvch gvani No. 3 otid go 7 respectively.