|
%I #17 Sep 16 2013 12:30:08
%S 0,3,8,15,20,24,35,48,63,80,84,99,120,128,143,144,168,180,195,224,240,
%T 243,255,275,288,308,320,323,360,384,399,440,468,483,495,528,560,575,
%U 600,624,648,660,675,728,735,768,783,819,840,884,899,960,975,1008
%N Numbers of the form x^2*y*(2*x + y).
%C (y^2 + 2*x*y - x^2)^4 + (2*x + y)*x^2*y*(2*x + 2*y)^4 = (x^4 + y^4 + 10*x^2*y^2 + 4*x*y^3 + 13*x^3*y)^2. The equation implies that for any n, x^4 + a(n)*y^4 = z^2 is solvable in integers.
%D L. E. Dickson, History of the Theory of Numbers, Vol. II. Diophantine analysis, Carnegie Institute of Washington, 1919. Reprinted by AMS Chelsea Publishing, New York, 1992, p. 631.
%t n = 1008; limx = Floor[(n/2)^(1/3)]; limy = Floor@Sqrt[n]; Select[Union@Flatten@Table[x^2*y*(2*x + y), {x, 0, limx}, {y, limy}], # <= n &]
%Y Cf. A218381.
%K nonn
%O 1,2
%A _Arkadiusz Wesolowski_, Sep 11 2013
|
