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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 x2. If p is a polynomial in n variables and p(x1, …, xn) = p(y1, …, yn) when x12 + … + xn2 = y12+ … + yn2 then p is a polynomial in q where q(x1, …, xn) = x12 + … + xn2.

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