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Liouville Polynomial Identity

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A Liouville polynomial identity is given by

6(x_1^2+x_2^2+x_3^2+x_4^2)^2=(x_1+x_2)^4+(x_1+x_3)^4+(x_2+x_3)^4+(x_1+x_4)^4+(x_2+x_4)^4+(x_3+x_4)^4+(x_1-x_2)^4+(x_1-x_3)^4+(x_2-x_3)^4+(x_1-x_4)^4+(x_2-x_4)^4+(x_3-x_4)^4.

This is proven in Rademacher and Toeplitz (1957).

See also

Waring's Problem

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References

Rademacher, H. and Toeplitz, O. The Enjoyment of Mathematics: Selections from Mathematics for the Amateur. Princeton, NJ: Princeton University Press, pp. 55-56, 1957.

Referenced on Wolfram|Alpha

Liouville Polynomial Identity

Cite this as:

Weisstein, Eric W. "Liouville Polynomial Identity." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LiouvillePolynomialIdentity.html

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