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Lebesgue Identity

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The Lebesgue identity is the algebraic identity

(a^2+b^2+c^2+d^2)^2=(a^2+b^2-c^2-d^2)^2+(2ac+2bd)^2+(2ad-2bc)^2

(Nagell 1951, pp. 194-195).

See also

Diophantine Equation--2nd Powers, Euler Four-Square Identity

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References

Nagell, T. Introduction to Number Theory. New York: Wiley, 1951.

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Lebesgue Identity

Cite this as:

Weisstein, Eric W. "Lebesgue Identity." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LebesgueIdentity.html

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