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Search: id:A046881
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| A046881 |
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Smallest number that is sum of 2 positive distinct n-th powers in 2 different ways. |
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+0
2
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OFFSET
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1,1
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COMMENT
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Randy Ekl discovered that a number that can be written in two ways as a sum of two fifth powers exceeds 2^74 and one that can be written in two ways as a sum of two sixth powers exceeds 2^89. - Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 28 2007
According to the Mathworld links below, a(5) and a(6), if they exist, exceed 1.02*10^26 and 7.25*10^26, respectively. The page at the SquaresOfCubes link below says Stuart Gascoigne did an exhaustive search and found in Sep 2002 that no a(5) solution less than 3.26*x10^32 exists. My exhaustive search has determined that any solutions for n > 5, if they exist, must exceed 2^96 (about 7.92x10^28). - Jon E. Schoenfield (jonscho(AT)hiwaay.net), Dec 15 2008
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REFERENCES
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R. Alter, Computations and generalizations on a remark of Ramanujan, pp. 182-196 of "Analytic Number Theory (Philadelphia, 1980)", ed. M. I. Knopp, Lect. Notes Math., Vol. 899, 1981.
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LINKS
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Christian Boyer, Squares of Cubes.
Weisstein, Eric W., Diophantine Equation--5th Powers [From Jon E. Schoenfield (jonscho(AT)hiwaay.net), Nov 27 2008]
Weisstein, Eric W., Diophantine Equation--6th Powers [From Jon E. Schoenfield (jonscho(AT)hiwaay.net), Nov 27 2008]
Tom Womack, Equal Sums of Like Powers.
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EXAMPLE
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5=1^1+4^1=2^1+3^1, 65=1^2+8^2=4^2+7^2, 1729=1^3+12^3=9^3+10^3, etc.
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CROSSREFS
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Cf. A016078.
Sequence in context: A079482 A147625 A157097 this_sequence A012635 A162080 A012476
Adjacent sequences: A046878 A046879 A046880 this_sequence A046882 A046883 A046884
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KEYWORD
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nonn,nice,hard
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)
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EXTENSIONS
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Added a link and added to my earlier comment. - Jon E. Schoenfield (jonscho(AT)hiwaay.net), Dec 15 2008
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