544 HISTORY OF THE THEORY OF NUMBERS. [CHAP, xx 



An identity (p. 253) shows that 4 times the cube of any even integer is a 

 G3 less a SO. 



G. de Longchamps 93 noted that ax 1 +$if+yz 1 +tt' i = u? for 



22 - 2 - 2 



/ g 



The case 5 = = gives Neuberg's result. 



An anonymous writer 94 noted the solution x = 3, y = l2, 2 = 11, u = 2 of 



J. Rose 95 noted the solution # = 4y 2 , 7/ = 4w 3 , z = kv 1 (v 1), it = 2y, and a 

 solution with y = z-\-l. Mehmed-Nadir gave the solution 



z = 6(a 2 +6 2 )(a 2 -fc 2 ); z, 7/ = |{(a 2 l)(a 2 +6 2 ) 2 46 4 } ; u = a*+V; 

 and noted that the same x, u, with F = a(a 2 +6 2 ) 2 , Z = 2a6 2 (a 2 +6 2 ), satisfy 



" V. G. Tariste" 96 stated that all sets of solutions of x 2 +if-z* = u 5 are 

 given by seven sets of formulas like ^ = 4a, x = 2b, u?x- = 4:a(3; y, 2 = 



F. L. Griffin and G. B. M. Zerr 96a discussed x\-\ ----- t-xl = y*. 

 W. H. L. Janssen van Raay 97 solved x z =x z -{-y 2 -{-z 2 . 



G. Candido 98 found a solution of 2x 2 i=y p by expanding H(a*+l3%). 

 R. D. Carmichael" gave a four-parameter solution of x 2 -\-ay 2 -\-bz 2 = 



93 L'interm4diaire des math., 10, 1903, 111-2. 

 "Ibid., 14, 1907,244. 

 96 Ibid., 15, 1908, 46. 



96 Ibid., 19, 1912, 38. 



960 Amer. Math. Monthly, 17, 1910, 147-8. 



97 Wiskundige Opgaven, 12, 1915, 209-11. 



98 Periodico di Mat., 30, 1915, 45-47. 



99 Diophantine Analysis, New York, 1915, 46. 



