Geodesic
On Polynomials with Related Level Sets
Canadian mathematical bulletin, Tome 13 (1970) no. 1, pp. 137-138

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Rosenfeld, M. On Polynomials with Related Level Sets. Canadian mathematical bulletin, Tome 13 (1970) no. 1, pp. 137-138. doi: 10.4153/CMB-1970-029-x
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[1] 1. Ahlfors, L. V., Complex analysis, McGraw-Hill, New York (second edition), 1966. Google Scholar

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