268 



Proof. Make in proposition 7 v = — 1 : tlien we have D„^). = 1, 

 8ince 1' — 1 = — 2 and k is odd. 

 Hence 



according to 4, V. Consequently 



Definition 7. If h be an integer >• 2, the coeflicients 5; and C; 

 I - > ;. > j are defined by the relation 



r 





^ S, ^> 

 and 



/ f!^^ 2 



;=o 



in which tiie [)rodiiels are extended over all the values <j and t of 

 a reduced rest-system, modulo k, for which | — j = -(- 1 and 



(i) 





Proposition 10. If k be an odd squareless number, we have 



2 2 



^ 5; 6„_|_; = and ^ C^ c„+; = 0, 

 ;=:0 A=o 



if we make 



and 



Z>'> being the G. C. D. of I and k. In these formulae n may be 

 any integer whatever. 



Proof. D\n is greater than 1, if ( — J = 0, according to 4, IV; 



consequently 



