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A232718
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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.
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0
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OFFSET
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1,1
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COMMENTS
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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.
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REFERENCES
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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.
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LINKS
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EXAMPLE
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1453978915260300^2 + 7518954988589021^2 = 7658246457672229^2;
(7518954988589021 - 1453978915260300)^2 - 2*1453978915260300^2 = 5705771236038721^2. - Bruno Berselli, Jun 27 2020
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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