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A034404
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Values of C(n,3) which can be written as C(x,3) + C(y,3).
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3
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20, 680, 29260, 34220, 70300, 221815, 227920, 287980, 467180, 908600, 2481115, 4278680, 12259940, 13813570, 15493204, 17861900, 19970444, 24672560, 25665020, 27880600, 29742164, 34055980, 44722580
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OFFSET
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1,1
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COMMENTS
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Bombieri's Napkin Problem: Bombieri said that "the equation C(x,n) + C(y,n) = C(z,n) has no trivial solutions for n >= 3" (the joke being that he said "trivial" rather than "nontrivial"!).
Also: tetrahedral numbers that are the sum of two other tetrahedral numbers. (For the indices of these terms, see A002311.) - Harvey P. Dale, Jul 25 2011
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REFERENCES
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Van der Poorten, Notes on Fermat's Last Theorem, Wiley, p. 122.
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LINKS
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FORMULA
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EXAMPLE
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C(10,3) + C(16,3) = C(17,3) = 680.
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MATHEMATICA
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With[{tetras=Binomial[Range[700]+2, 3]}, Union[Select[Total/@Tuples[ tetras, 2], MemberQ[tetras, #]&]]] (* Harvey P. Dale, Jul 25 2011 *)
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PROG
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(Haskell)
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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