64 ON THE ALGEBRAICAL SOLUTION OF 



. (3) 



Adding now corresponding sides of (2) and (3) and omitting 

 the terms which are common to both sides we obtain 



For example, x v =x^=y^=\, ^=2 gives 



2 4 + 8 4 + 18 4 + 33 4 = 6 4 + 14 4 + 24 4 + 31 4 . 

 Again, we have identically 



Multiplying corresponding sides of these equations together 

 we obtain 



which is an algebraical solution of the equation 



P 1 4 +P 2 4 +P 3 4 +P 4 4 +P 5 4 =P' 1 4 +P' 

 Again, we have identically 



4 2 4 



~ 

 * 

 ~ 



Hence by subtraction we get 



r, 4 . 4 \ 4 





-w 7; 



Also s = s- =4. 



* 



