A070066 Values of y in positive integer solutions of x^2 + y^5 = z^3, listed in increasing order of z. (If a z-value occurs twice, list solutions in increasing order of y.)

3, 9, 16, 16, 32, 48, 24, 6, 55, 72, 72, 100, 72, 112, 72, 108, 144, 162, 36, 192, 72, 100, 216, 72, 295, 343, 351, 359, 72, 368, 423, 343, 216, 300, 343, 648, 800, 783, 625, 833, 400, 450, 648, 972, 496, 576, 1024, 864, 675, 972, 1215, 242, 72, 500, 1176

Offset: 1

Author

Dean Hickerson and Dan Asimov (asimov(AT)msri.org), Apr 18 2002

Keywords

• nonn

Examples

			The first 5 solutions are (x,y,z) = (10,3,7), (1242,9,117), (1024,16,128), (5632,16,320) and (20480,32,768).
		

Crossrefs

x-values are in A070065, z-values are in A070067.

Programs

Mathematica

For[z=1, True, z++, z3=z^3; For[y=1, (d=z3-y^5)>0, y++, If[IntegerQ[x=Sqrt[d]], Print[{x, y, z}]]]]