A103268 -id:A103268 - cp's OEIS frontend

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A114737 Positive integers x such that there exist positive integers y >= x and z satisfying x^3 + y^3 = z^5.

Original entry on oeis.org

3, 8, 96, 256, 624, 686, 729

Offset: 1

N. J. A. Sloane, Jan 31 2007

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

			x=3, y=6, 3^3 + 6^3 = 3^5, so 3 is a term.
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

F. Beukers, The Diophantine equation Ax^p+By^q=Cz^r, Duke Math. J. 91 (1998), 61-88.
Nils Bruin, On powers as sums of two cubes, in Algorithmic number theory (Leiden, 2000), 169-184, Lecture Notes in Comput. Sci., 1838, Springer, Berlin, 2000.

See A103268 for another version.

Term 624 added by Chai Wah Wu, Jan 11 2016

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