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A229076 Euler's fearsome foursome. 1

%I

%S 18530,38114,45986,65570

%N Euler's fearsome foursome.

%C Four distinct positive integers the sum of any two of which is a square, two of the squares being equal.

%C Dunham calls them "Euler's fearsome foursome", but neglects to require that two of the sums be equal. Liu requires it and explains Euler's derivation.

%D W. Dunham, Euler: The Master of Us All, MAA, 1999, p. 7.

%D L. Euler, Opera Omnia, vol. 5, pp. 337 - 339, supplement to Paper 796.

%H Paul Liu, <a href="http://math.fau.edu/yiu/eulernotes99.pdf">The Elementary Mathematical Works of Leonhard Euler (1707 - 1783)</a>, pp. 129-133.

%e If (A, B, C, D) = (18530, 38114, 45986, 65570), then A+D = B+C = 290^2, A+C = 254^2, C+D = 334^2, A+B = 238^2, and B+D = 322^2.

%Y Cf. A229077.

%K nonn,fini,full

%O 1,1

%A _Jonathan Sondow_, Sep 12 2013

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Last modified January 18 00:56 EST 2022. Contains 350410 sequences. (Running on oeis4.)