Search: id:A114737
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%I A114737
%S A114737 3,8,96,256,686,729
%N A114737 Positive integers x such that there exist positive integers y >= x and 
               z satisfying x^3 + y^3 = z^5.
%C A114737 Warning! These terms have not been proved to be correct. There may be 
               missing terms.
%C A114737 There are no solutions with (x,y,z) relatively prime. [Bruin]
%D A114737 F. Beukers, The Diophantine equation Ax^p+By^q=Cz^r, Duke Math. J. 91 
               (1998), 61-88.
%D A114737 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.
%e A114737 x=3, y=6, 3^3 + 6^3 = 3^5, so 3 is a member.
%e A114737 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
%Y A114737 See A103268 for another version.
%Y A114737 Sequence in context: A079657 A136309 A069703 this_sequence A099296 A066619 
               A028504
%Y A114737 Adjacent sequences: A114734 A114735 A114736 this_sequence A114738 A114739 
               A114740
%K A114737 more,nonn
%O A114737 1,1
%A A114737 N. J. A. Sloane (njas(AT)research.att.com), Jan 31 2007

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