( 74) 



CO 



approaching from the right side lun V^ — exists and is equal to 



00 



'V* — . Making use of (12), (5) and (6) we find therefore 





"" ^ (è) (^ Z^ Z^ Xv {h) L.. (1) * 



§ 8. In this paragraph must be proved the lemma: 

 When Qb,h{x) denotes the number of the integers without quadratic 

 factors ^x belonging to the linear form mh-\-h (where (b,h)^d 

 is supposed to be without quadratic factors ^) ), then 



,. Qm(-^-) 



iim 



1=00 •^' 



exists and has a value differing from zero. 



I. Let us suppose (h, h)^= d = 1 first. Let Ao^h.ni^) denote the 

 number of those integers m which fulfill the congruence 



^^ + ^i ^ ^ {mod. 7l) 



and the unequalities 



,x — k 



(i. e. 1 ^mb -\- h^ x). Then it is evident when n possesses with 

 b a common factor that on account of {b, Ii) = 1 the congruence 

 cannot be solved; so 



Am(-^') = (18) 



When however (?i, b) = l the congruence has modulo n exactly 



,v — A 

 one root ; so the number of roots between and — — is equal to 



r^-h^b-] p-/t+6-| . 



Atxn{ci^) = ^ + ^ (-1<^<2) (19) 



on 



Now it is evident that when k passes through every number the 



1) In the opposite case Qt.k (x) = 0. 



