1,1

Warning: these entries have not been proved to be correct! There may be missing terms. - N. J. A. Sloane (njas(AT)research.att.com), Jan 05 2007

Conjecture: The greatest prime divisor of x divides y and z.

Many of these values are derived from the essentially trivial solution {x,y,z} ={(a + b)*b*(3*a^2 + 3*a*b + b^2), a*b*(3*a^2 + 3*a*b + b^2), b*(3*a^2 + 3*a*b + b^2)}. This solution follows from the fact that (a+b)^3-a^3 = b*(3*a^2 + 3*a*b + b^2) and that multiplying this equation by [b*(3*a^2 + 3*a*b + b^2)]^3 gives a solution to y^3 - x^3 = z^4. - James McLaughlin, Jan 27 2007

F. Beukers, The Diophantine equation Ax^p+By^q=Cz^r, Duke Math. J. 91 (1998), 61-88.

x=762, y=889, 889^3 - 762^3 = 127^4, so 762 is on the list.

Other solutions: (x,y,z) = (26, 26, 78), (38, 19, 57), (63, 63, 252), (111, 37, 148), (112, 56, 224), (124, 124, 620), (207, 126, 639), (215, 215, 1920), (234, 117, 585), (244, 61, 305), (294, 98, 490), (342, 342, 2394), (368, 161, 897), (416, 208, 1248), (455, 91, 546), (567, 189, 1134), (608, 152, 912), (670, 335, 2345), (762, 127, 889), (948, 316, 2212), (1090, 218, 1526), (1116, 279, 1953), (1183, 169, 1352), (1736, 217, 1953), (1776, 296, 2368), (2119, 273, 2470), (2439, 271, 2710), ...

Sequence in context: A098127 A131905 A110927 this_sequence A125972 A063153 A063578

Adjacent sequences: A103264 A103265 A103266 this_sequence A103268 A103269 A103270

nonn

Cino Hilliard (hillcino368(AT)gmail.com), Mar 20 2005