A070065 Values of x 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.)

10, 1242, 1024, 5632, 20480, 17920, 37376, 39151, 36599, 15552, 26001, 75000, 124416, 68608, 172800, 209952, 359424, 413343, 579096, 327680, 684288, 1090625, 1306368, 1650240, 1506463, 1529437, 1607445, 1525899, 3637224, 2783744

Offset: 1

Author

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

Keywords

• nonn

Comments

If x is in the sequence, then so is c^15 x for positive integers c, since if (x,y,z) is a solution, so is (c^15 x, c^6 y, c^10 z). - Robert Israel, Jul 26 2017

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

y-values are in A070066, 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}]]]]