Factorizable Continuants. 33 



Putting x= - b we have verification that the continuant is resolvable 

 into 



(a - 3b) (a-2b-c)(a-b- 2c) (a - 3c). 



Putting x = - c we have a second verification, the factors being now 

 got in the reverse order. 



In the third place, the putting of x = and x — b brings out the 

 identity of Painvin's continuant and that referred to in § 4 : the 

 number of such identities, however, is seen to be infinite. 



Lastly, the sum of the diagonal elements being independent of x 

 is the same when x = as when x = - b : there is thus verified the 

 assertion of § 3 regarding the sum of the factors in the result. 



^ 



