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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 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=1..8.

A. Aigner, Review (in German) of G. Gatti's "Su un problema di Fermat", zbMATH Zbl 0529.10020.

A. Aigner, Review (in German) of C. Viola's "Commento al N.44 delle `Osservazioni su Diofanto' di Fermat", zbMATH Zbl 0529.10021.

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

Adjacent sequences:  A232715 A232716 A232717 * A232719 A232720 A232721

KEYWORD

nonn,hard,more

AUTHOR

Jonathan Sondow, Dec 03 2013

EXTENSIONS

a(5) corrected by Bruno Berselli, Jun 27 2020

STATUS

approved

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Last modified May 27 16:48 EDT 2022. Contains 354110 sequences. (Running on oeis4.)