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A192631
Numerators of the Diophantus-Dujella rational Diophantine quintuple: 1 + the product of any two distinct terms is a square.
4
1, 33, 17, 105, 549120
OFFSET
1,2
COMMENTS
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.
REFERENCES
E. Herrmann, A. Pethoe and H. G. Zimmer, On Fermat's quadruple equations, Abh. Math. Sem. Univ. Hamburg 69 (1999), 283-291.
EXAMPLE
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.
CROSSREFS
KEYWORD
nonn,fini,frac
AUTHOR
Jonathan Sondow, Jul 07 2011
STATUS
approved