MathDB

For every non-constant polynomial

p

, let

H_p=\big\{z\in \mathbb{C} \, \big| \, |p(z)|=1\big\}

. Prove that if

H_p=H_q

for some polynomials

p,q

, then there exists a polynomial

r

such that

p=r^m

and

q=\xi\cdot r^n

for some positive integers

m,n

and constant

|\xi|=1

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