A232718 - OEIS

A232718

Solutions a < d < b < c of Fermat's system of Diophantine equations a^2 + b^2 = c^2 and (a-b)^2 - 2*a^2 = d^2.

%I #13 Jun 28 2020 02:49:03

%S 156,1343,1517,1525,1453978915260300,5705771236038721,

%T 7518954988589021,7658246457672229

%N Solutions a < d < b < c of Fermat's system of Diophantine equations a^2 + b^2 = c^2 and (a-b)^2 - 2*a^2 = d^2.

%C Fermat gave the smallest solution (a, d, b, c) = (156, 1343, 1517, 1525). Viola found the second smallest, using elliptic curves. See Aigner's zbMATH reviews.

%D Guido Gatti, Su un problema di Fermat, Archimede, 35 (1983), 177-178.

%D Carlo Viola, Commento al N.44 delle "Osservazioni su Diofanto" di Fermat, Archimede, 35 (1983), 179-185.

%H A. Aigner, <a href="http://zbmath.org/scans/529/043.gif">Review (in German) of G. Gatti's "Su un problema di Fermat"</a>, zbMATH Zbl 0529.10020.

%H A. Aigner, <a href="http://zbmath.org/scans/529/043.gif">Review (in German) of C. Viola's "Commento al N.44 delle `Osservazioni su Diofanto' di Fermat"</a>, zbMATH Zbl 0529.10021.

%e 1453978915260300^2 + 7518954988589021^2 = 7658246457672229^2;

%e (7518954988589021 - 1453978915260300)^2 - 2*1453978915260300^2 = 5705771236038721^2. - _Bruno Berselli_, Jun 27 2020

%Y Cf. A138604.

%K nonn,hard,more

%O 1,1

%A _Jonathan Sondow_, Dec 03 2013

%E a(5) corrected by _Bruno Berselli_, Jun 27 2020