A192630 Denominators of the Fermat-Euler rational Diophantine m-tuple.

1, 1, 1, 1, 1, 8288641

Offset

0,6

Comments

Fermat gave the integer Diophantine m-tuple 1, 3, 8, 120 (see A030063): 1 + the product of any two distinct terms is a square. Euler added the rational number 777480/8288641.

Stoll proved that an extension of Fermat's set to a rational quintuple with the same property is unique. - Andrej Dujella, May 12 2024

Numerators are A192629.

See A030063 and A192629 for additional comments, references, and links.

Links

Table of n, a(n) for n=0..5.

Michael Stoll, Diagonal genus 5 curves, elliptic curves over Q(t), and rational diophantine quintuples, Acta Arith. 190 (2019), 239-261.

Example

0/1, 1/1, 3/1, 8/1, 120/1, 777480/8288641.
1 + 1*(777480/8288641) = (3011/2879)^2.

Crossrefs

Cf. A030063, A192629, A192631, A192632.

Sequence in context: A233484 A363792 A234383 * A379179 A098809 A011573

Adjacent sequences: A192627 A192628 A192629 * A192631 A192632 A192633

Keyword

nonn,fini,full,frac

Author

Jonathan Sondow, Jul 06 2011

Status

approved