A192630 - OEIS

%I #21 Jun 01 2024 23:52:00

%S 1,1,1,1,1,8288641

%N Denominators of the Fermat-Euler rational Diophantine m-tuple.

%C 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.

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

%C Numerators are A192629.

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

%H Michael Stoll, <a href="https://doi.org/10.4064/aa180416-4-10">Diagonal genus 5 curves, elliptic curves over Q(t), and rational diophantine quintuples</a>, Acta Arith. 190 (2019), 239-261.

%e 0/1, 1/1, 3/1, 8/1, 120/1, 777480/8288641.

%e 1 + 1*(777480/8288641) = (3011/2879)^2.

%Y Cf. A030063, A192629, A192631, A192632.

%K nonn,fini,full,frac

%O 0,6

%A _Jonathan Sondow_, Jul 06 2011