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

Csóké Lajos: Sturm tételének gyakorlati alkalmazásáról.

- AO ! least index with such property by rCp), i.e. rCp)=n if pJR but P-tR

m for 0<m<n. In this case wo say p ÍB a primitive prime divisor of R^. For primes p with pjB there is no term R^Cn^l) divisible by p if CA,B)=ij in this case we assume r(p)=oo. If p is a prime, pjB, D«A

2+4B and CD/p) denotes the Legendre's symbol with CD/p)=0 if pjD then, as it is well known

, C2) rCp) I Cp - CD/p)) and C 3 ) p I R^ if and only if rCp)jn (see e.g. t 2 3). In the special case CAjB)=C3j-2) the terms of the sequence R are R^=2

n—

1. For this sequence P,

Erdős El 3 proved that there are positive constants c'and c'

' such that 4 2 - < log log log II + c" p|C2"~l) for the distinct prime divisors and 5 ^ < c" . log log n d|(2

n-l) for the distinct positive divisors of the t.er»n«. Erdős noted that similar results hold for the divisors of the numbers a

n-l Ca>l is an integer) but he asked wether the constants c* and c*

' in this case depend on a or not. In this paper, using a little modification of Erdős* argument, - we extend these ' results for Lucas numbers furthermore we give their improvements by showing that the constants in the inequalities do not depend on the sequence. We note that R if n^O (since cx/

73 is not a root of ri ' unity) and we shall write i for the reciprocal sum of the divisors of R if R =1.