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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 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=1..5.

A. Dujella, Rational Diophantine m-tuples

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

Cf. A030063, A192629, A192630, A192632.

Sequence in context: A200897 A138839 A033353 * A104781 A159001 A304261

Adjacent sequences:  A192628 A192629 A192630 * A192632 A192633 A192634

KEYWORD

nonn,fini,frac

AUTHOR

Jonathan Sondow, Jul 07 2011

STATUS

approved

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Last modified January 16 01:34 EST 2021. Contains 340195 sequences. (Running on oeis4.)