92 ALGEBRAICAL SOLUTION OF EQUATIONS 



formula can be found to satisfy equation (1). For we have 

 identically 



If then we put t=x 2 +xy+y 2 this becomes 

 [(x*+xy+y*) z +z i ]*=(x z +xy+y*)*+ ( z *)*+z*[x*+y*+Jc+y*]. (7) 

 Since x and y are arbitrary we may take (as in 4 supra) 



x=Qi, y=Q z , 



where Q l and Q z are algebraical quantities satisfying the 

 equation 



where r is greater than 2. Hence (7) becomes 



+ . . . +P*) 



which gives a square equal to the sum of 5 or any greater 

 number of biquadrates. 



ROBERT NOEEIE 



