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

Csóké Lajos: Sturm tételének gyakorlati alkalmazásáról.

Comparing C l 3) w ith Ci4> c x C15) qíi,3í) < 5 2

l • log x follows? for 12:4. I.of. ,i(m) bo an arithmetical function mich that nCriO«»! if m is a prime satisfying the conditions for the primes in k 5 and aCm)~0 otherwise. Then i. 2 a<m) ^ qCi,x) m^x by the definiton of qCi,x) and, using C15) and the fact y ;

J,™y j" , by Abel's identity we have C

16:> 2 t ~ I aCm)'i . p m y: c 2 dt " ' J < 2

2v 1 • log log n y 1 flog t 2

V for any i2:4L. But by C8> = 0C1) ^ \ P i R P P LTogrVj í =o páClog n> p-^log n since p£d—

1 if rCp)=d, and so by CO) and C16) we obtain C17) A'Cn) « c® 5 K- + 0C1) < c . 2 O ~ t 1 O t A For the third summand of ACn) we also get A^Cn)=OCi>. Namely R has at most k^i/log n distinct prime divisors greater than n, and so really 1 <? k n C18) A (n) 5 J L < L . i—. < c 3 P n . ^ it p 1R l

o£ n ' ' n p>n if n is sufficiently large. Thus by Cő), C9), Cll), Ci7) arid CIO)