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Search: id:A103255
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| A103255 |
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Positive integers x such that there exist positive integers y and z satisfying x^3 + y^3 = z^2 and gcd(x,y) = 1. |
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+0
3
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OFFSET
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1,2
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REFERENCES
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F. Beukers, The Diophantine equation Ax^p+By^q=Cz^r, Duke Math. J. 91 (1998), 61-88.
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LINKS
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H. Darmon and A. Granville, On the equations z^m=F(x,y) and Ax^p+By^q=Cz^r, Bull. Lond. Math. Soc., 27 (6) (1995) 513, Sect 7.2.
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EXAMPLE
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x=11, y=37, 11^3 + 37^3 = 228^2. 11 is the third entry in the list.
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PROGRAM
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(MAGMA) [ k : k in [1..100] | exists{P : P in IntegralPoints(EllipticCurve([0, k^3])) | P[1] gt 0 and P[2] ne 0 and GCD(Integers()!P[1], k) eq 1} ]; (from Geoff Bailey)
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CROSSREFS
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Adjacent sequences: A103252 A103253 A103254 this_sequence A103256 A103257 A103258
Sequence in context: A085745 A106856 A045387 this_sequence A031385 A126916 A056637
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KEYWORD
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easy,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Mar 20 2005
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EXTENSIONS
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Recomputed and extended by Geoff Bailey (geoff(AT)maths.usyd.edu.au) using MAGMA, Jan 28 2007.
a(9)-a(10) from Jonathan Vos Post (jvospost2(AT)yahoo.com), May 27 2007
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