
COMMENTS

Warning! These terms have not been proved to be correct. There may be missing terms.
There are no solutions with (x,y,z) relatively prime. [Bruin]
For max(x,y) < 1.1*10^12, there are no more terms < 1458. Most likely this is true for all x,y.  Chai Wah Wu, Jan 15 2016


LINKS

Table of n, a(n) for n=1..7.
F. Beukers, The Diophantine equation Ax^p+By^q=Cz^r, Duke Math. J. 91 (1998), 6188.
Nils Bruin, On powers as sums of two cubes, in Algorithmic number theory (Leiden, 2000), 169184, Lecture Notes in Comput. Sci., 1838, Springer, Berlin, 2000.


EXAMPLE

x=3, y=6, 3^3 + 6^3 = 3^5, so 3 is a member.
With max(x,y) < 10^4, we have these [x,y,z] triples: [3, 6, 3] [8, 8, 4] [96, 192, 24] [256, 256, 32] [729, 1458, 81] [1944, 1944, 108] [686, 2058, 98] [3696, 4368, 168] [3072, 6144, 192] [8192, 8192, 256] [2508, 8436, 228] ...  David Broadhurst
624^3 + 14352^3 = 312^5.  Chai Wah Wu, Jan 11 2016
