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Search: id:A086302
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| A086302 |
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4*n^4 + 24*n^3 + 48*n^2 + 36*n + 8. |
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+0
3
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| 8, 120, 528, 1520, 3480, 6888, 12320, 20448, 32040, 47960, 69168, 96720, 131768, 175560, 229440, 294848, 373320, 466488, 576080, 703920, 851928, 1022120, 1216608, 1437600, 1687400, 1968408, 2283120, 2634128, 3024120, 3455880, 3932288, 4456320, 5031048
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Suppose one wishes to find sets of four positive integers (a,b,c,d) so that ab+1, ac+1, ad+1, bc+1, bd+1, cd+1 are perfect squares. Then one may take a = 1, b = x^2 + 2x, c = x^2 + 4x + 3, d = 4x^4 + 24x^3 + 48x^2 + 36x + 8.
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LINKS
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P. Gibbs, Diophantine quadruples and Cayley's hyperdeterminant.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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EXAMPLE
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(a,b,c,d) = (1,3,8,120) (1,8,15,528) (1,15,24,1520) (1,24,35,3480) ...
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CROSSREFS
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Equals A057769(n+1) + 1.
Sequence in context: A085699 A046914 A116008 this_sequence A053129 A045899 A165231
Adjacent sequences: A086299 A086300 A086301 this_sequence A086303 A086304 A086305
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KEYWORD
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nonn
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AUTHOR
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Neven Juric (neven.juric(AT)apis-it.hr), Aug 29 2003
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