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

Csóké Lajos: Sturm tételének gyakorlati alkalmazásáról.

t l+i (log ri) < p Clog n>

2 and For which the conditons in C10>

: are sntisf ied. Ve? nol.e that OC1/log n) in C12) can be different from zero only if there ir* a prime p such that log n — 1 < p ^ log n , rCp)=p+l and Cp+i)|n. Since rCp)=d, d|n and p<d

* for the I, primes in ^ , by (2), Cp-CD/p)

,n) £ d > Y p > [log n)

2' follows and (D/pi^O if n Is large. Let x be a real number with conditons y^ (log n) < x 5 Clog n> = y and let Q(.i,x) be a set of primes p defined by Q(i,x) = |p : p<x, Cp-CD/p>, n) > [log nj

2'

/

3 j . If qC i

,x) denotes the cardinality of the set QCi,x), then evidently C13) 1 T Cp-CD/p>, n) > [log p<x On the other hand Erdős proved that 1 T Cp-i , n> < exp [c^x'log log n/log xj p<x for any x>Clog n)

i

c and xin Csee CIS) and C21) in Ell) and we can similarly obtain that 1 T Cp+1 , n) < exp ^c

cx*log log n/log xj , p<x thus C14) T~T Cp-CD/p) , n) < 1 T Cp-i , n) • Cp+1 , n> < p<x p<x < exp |c

7x*log log »/log xj .