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A192631
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Numerators of the Diophantus-Dujella rational Diophantine quintuple: 1 + the product of any two distinct terms is a square.
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4
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OFFSET
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1,2
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COMMENTS
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Denominators are A192632. Diophantus found the rational Diophantine quadruple 1/16, 33/16, 17/4, 105/16. Dujella added a fifth rational number 549120/10201.
It is unknown whether this rational Diophantine quintuple can be extended to a sextuple. Herrmann, Pethoe, and Zimmer proved that the sequence is finite, but no bound on its length is known.
See A030063 for additional comments, references, and links.
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REFERENCES
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E. Herrmann, A. Pethoe and H. G. Zimmer, On Fermat's quadruple equations, Abh. Math. Sem. Univ. Hamburg 69 (1999), 283-291.
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LINKS
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Table of n, a(n) for n=1..5.
A. Dujella, Rational Diophantine m-tuples
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EXAMPLE
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1/16, 33/16, 17/4, 105/16, 549120/10201.
1 + (1/16)*(33/16) = (17/16)^2.
1 + (33/16)*(549120/10201) = (1069/101)^2.
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CROSSREFS
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Cf. A030063, A192629, A192630, A192632.
Sequence in context: A200897 A138839 A033353 * A104781 A159001 A304261
Adjacent sequences: A192628 A192629 A192630 * A192632 A192633 A192634
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KEYWORD
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nonn,fini,frac
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AUTHOR
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Jonathan Sondow, Jul 07 2011
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STATUS
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approved
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