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%I #11 Sep 07 2013 14:30:48
%S 1,33,17,105,549120
%N Numerators of the Diophantus-Dujella rational Diophantine quintuple: 1 + the product of any two distinct terms is a square.
%C 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.
%C 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.
%C See A030063 for additional comments, references, and links.
%D E. Herrmann, A. Pethoe and H. G. Zimmer, On Fermat's quadruple equations, Abh. Math. Sem. Univ. Hamburg 69 (1999), 283-291.
%H A. Dujella, <a href="http://web.math.hr/~duje/ratio.html">Rational Diophantine m-tuples</a>
%e 1/16, 33/16, 17/4, 105/16, 549120/10201.
%e 1 + (1/16)*(33/16) = (17/16)^2.
%e 1 + (33/16)*(549120/10201) = (1069/101)^2.
%Y Cf. A030063, A192629, A192630, A192632.
%K nonn,fini,frac
%O 1,2
%A _Jonathan Sondow_, Jul 07 2011
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