A229076 Euler's fearsome foursome.

18530, 38114, 45986, 65570

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

Table of n, a(n) for n=1..4.

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

Cf. A229077.

Sequence in context: A237012 A031817 A236816 * A157740 A248488 A237700

Adjacent sequences: A229073 A229074 A229075 * A229077 A229078 A229079

Keyword

nonn,fini,full

Author

Jonathan Sondow, Sep 12 2013

Status

approved