Search: id:A020898
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%I A020898
%S A020898 2,6,7,9,12,13,15,17,19,20,22,26,28,30,31,33,34,35,37,42,43,49,50,
%T A020898 51,53,58,61,62,63,65,67,68,69,70,71,75,78,79,84,85,86,87,89,90,91,
%U A020898 92,94,97,98,103,105,106,107,110,114,115,117,123,124,126,127,130
%N A020898 Positive (and cube-free) integers n such that the Diophantine equation 
               X^3 + Y^3 = n*Z^3 has integer solutions.
%C A020898 These numbers are the cube-free sums of two nonzero rational cubes.
%D A020898 J. H. E. Cohn, The \pounds 450 question, Math. Mag., 73 (no. 3, 2000), 
               220-226.
%D A020898 B. N. Delone and D. K. Faddeev, The Theory of Irrationalities of the 
               Third Degree, Amer. Math. Soc., 1964.
%D A020898 L. E. Dickson, History of The Theory of Numbers, Vol. 2, Chap. XXI, Chelsea 
               NY 1966.
%D A020898 L. J. Mordell, Diophantine Equations, Ac. Press, Chap. 15.
%H A020898 S. R. Finch, <a href="http://algo.inria.fr/csolve/fermat.pdf">On a Generalized 
               Fermat-Wiles Equation</a>
%e A020898 37^3 + 17^3 = 6*21^3 is the smallest positive solution for n = 6 (found 
               by Lagrange)
%e A020898 5^3 + 4^3 = 7*3^3 is the smallest positive solution for n = 7.
%Y A020898 Sequence in context: A079335 A061416 A020897 this_sequence A047277 A109783 
               A030309
%Y A020898 Adjacent sequences: A020895 A020896 A020897 this_sequence A020899 A020900 
               A020901
%K A020898 nonn,nice
%O A020898 1,1
%A A020898 Steven.Finch(AT)inria.fr (S. R. Finch)
%E A020898 Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Aug 12 2004
%E A020898 Links updated by Max Alekseyev, Oct 17 2007 and Dec 12 2007

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