J(î Art. 5.— T. Takenouchi; 



Thu;^ we obtain 



9 G 



/^ .-. 

 Lastly, let D^ be the discriminant of the equation /iSV(//) = 

 regarded as an equation for 



yl ' 



Then wo can shew without any difficulty that 



— n ^ 



Avhence follows 



B.= D.,—, ^, 



(,„-l ) („,-7 ) w- 



Hitherto Ave have supposed that /'- is a primary integer. Uut, 

 the same method of calculating the discriminants can also be 

 applied to the case where ,« is a composite integer, provided that it 

 is odd. The result is exactly the same as in the above case. But; 

 it must be observed that the equation A„{x)=0 in this case is not 

 irreducible. The corpus of /^-division is determined Ity a root of 

 the equation of the v"(/^)th degree 



A',(x) = 0, 



where ^-J'.(^') is an irreducible factor of A,{}-). The abo\e method 

 cannot give the discriminant of this latter equation. For, if /^ be 

 not a prime, then in the form 



71 ±V = -^ — , 



ii 



the numerator may have a common di\'isor with /'-, without being 

 divisible by <« ; and consequently sn(?/±?') is not necessarily a root of 

 A'.ix) = 0. 



