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On Polynomials with Related Level Sets

Published online by Cambridge University Press:  20 November 2018

M. Rosenfeld
M. Rosenfeld*
Affiliation:
University of California, Santa Barbara, California
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If p is a polynomial in one real variable and p(x) = p(-x) then p has only even powers of x and is thus a polynomial in x 2. If p is a polynomial in n variables and p(x 1, …, x n ) = p(y 1, …, y n ) when x 1 2 + … + x n 2 = y 1 2+ … + y n 2 then p is a polynomial in q where q(x 1, …, x n ) = x 1 2 + … + x n 2.

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 13 , Issue 1 , March 1970, pp. 137 - 138
Copyright
Copyright © Canadian Mathematical Society 1970

References

1. Ahlfors, L. V., Complex analysis, McGraw-Hill, New York (second edition), 1966.Google Scholar