A192631 Numerators of the Diophantus-Dujella rational Diophantine quintuple: 1 + the product of any two distinct terms is a square.

1, 33, 17, 105, 549120

Offset: 1

Author

Jonathan Sondow, Jul 07 2011

Keywords

• nonn
• fini
• frac

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.

Examples

			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.
		

References

• E. Herrmann, A. Pethoe and H. G. Zimmer, On Fermat's quadruple equations, Abh. Math. Sem. Univ. Hamburg 69 (1999), 283-291.

Links

• A. Dujella, Rational Diophantine m-tuples

Crossrefs

Cf. A030063, A192629, A192630, A192632.