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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.
0
156, 1343, 1517, 1525, 1453978915260300, 5705771236038721, 7518954988589021, 7658246457672229
OFFSET
1,1
COMMENTS
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.
REFERENCES
Guido Gatti, Su un problema di Fermat, Archimede, 35 (1983), 177-178.
Carlo Viola, Commento al N.44 delle "Osservazioni su Diofanto" di Fermat, Archimede, 35 (1983), 179-185.
EXAMPLE
1453978915260300^2 + 7518954988589021^2 = 7658246457672229^2;
(7518954988589021 - 1453978915260300)^2 - 2*1453978915260300^2 = 5705771236038721^2. - Bruno Berselli, Jun 27 2020
CROSSREFS
Cf. A138604.
Sequence in context: A156994 A304619 A204718 * A204957 A263305 A235849
KEYWORD
nonn,hard,more
AUTHOR
Jonathan Sondow, Dec 03 2013
EXTENSIONS
a(5) corrected by Bruno Berselli, Jun 27 2020
STATUS
approved