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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. 1
3, 8, 96, 256, 624, 686, 729 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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), 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.

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

CROSSREFS

See A103268 for another version.

Sequence in context: A136309 A266671 A069703 * A233163 A281709 A099296

Adjacent sequences:  A114734 A114735 A114736 * A114738 A114739 A114740

KEYWORD

more,nonn

AUTHOR

N. J. A. Sloane, Jan 31 2007

EXTENSIONS

Term 624 added by Chai Wah Wu, Jan 11 2016

STATUS

approved

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Last modified June 21 07:27 EDT 2021. Contains 345358 sequences. (Running on oeis4.)