OFFSET

1,1

COMMENTS

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

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.

REFERENCES

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

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

LINKS

Paul Liu, The Elementary Mathematical Works of Leonhard Euler (1707 - 1783), pp. 129-133.

EXAMPLE

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.

CROSSREFS

KEYWORD

nonn,fini,full

AUTHOR

Jonathan Sondow, Sep 12 2013

STATUS

approved