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

Csóké Lajos: Sturm tételének gyakorlati alkalmazásáról.

k , k

2

> ... , which depend on the sequence R. First we consider inequality Cd). Let ACn) =2 £ • p|R By C3) we can write ACn) - J 2 £ • d jn rCp)-=d and ACn) can be divided into three parts: A.oo =2 If; djr» rCp)=d d^iog n and A

2cn> =2 If; d j n r C p)=d d>log n pSn A (n ) => 2 I ~ dIn rC p)-d d>log n p>n such that C6

) ACn) = A Cn) + A Cn) + A Cn). 12 3 By CI) and C2) it is easy to see that there are at most k^d^log d primes such that rCp)=d, so the number of primes in sum A Cn) is at most Clog n)'k

t' iog°íog n = ki * Íog°íog n ' It implies, using the estimation p^

< c

ii*log i for the i prime, that 1 h