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Search: id:A020898
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| A020898 |
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Positive (and cube-free) integers n such that the Diophantine equation X^3 + Y^3 = n*Z^3 has integer solutions. |
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+0
2
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| 2, 6, 7, 9, 12, 13, 15, 17, 19, 20, 22, 26, 28, 30, 31, 33, 34, 35, 37, 42, 43, 49, 50, 51, 53, 58, 61, 62, 63, 65, 67, 68, 69, 70, 71, 75, 78, 79, 84, 85, 86, 87, 89, 90, 91, 92, 94, 97, 98, 103, 105, 106, 107, 110, 114, 115, 117, 123, 124, 126, 127, 130
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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These numbers are the cube-free sums of two nonzero rational cubes.
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REFERENCES
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J. H. E. Cohn, The \pounds 450 question, Math. Mag., 73 (no. 3, 2000), 220-226.
B. N. Delone and D. K. Faddeev, The Theory of Irrationalities of the Third Degree, Amer. Math. Soc., 1964.
L. E. Dickson, History of The Theory of Numbers, Vol. 2, Chap. XXI, Chelsea NY 1966.
L. J. Mordell, Diophantine Equations, Ac. Press, Chap. 15.
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LINKS
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S. R. Finch, On a Generalized Fermat-Wiles Equation
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EXAMPLE
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37^3 + 17^3 = 6*21^3 is the smallest positive solution for n = 6 (found by Lagrange)
5^3 + 4^3 = 7*3^3 is the smallest positive solution for n = 7.
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CROSSREFS
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Sequence in context: A079335 A061416 A020897 this_sequence A047277 A109783 A030309
Adjacent sequences: A020895 A020896 A020897 this_sequence A020899 A020900 A020901
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KEYWORD
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nonn,nice
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AUTHOR
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Steven.Finch(AT)inria.fr (S. R. Finch)
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EXTENSIONS
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Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Aug 12 2004
Links updated by Max Alekseyev, Oct 17 2007 and Dec 12 2007
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