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4

Part of 2004 Romania Team Selection Test

Problems(1)

problem from the romanian team selection test 2004

Source: Romanian ROM TST 2004, problem 4, created by Dan Schwarz &am

5/1/2004
Let DD be a closed disc in the complex plane. Prove that for all positive integers nn, and for all complex numbers z1,z2,…,zn∈Dz_1,z_2,\ldots,z_n\in D there exists a z∈Dz\in D such that zn=z1⋅z2⋯znz^n = z_1\cdot z_2\cdots z_n.
logarithmsgeometrycircumcirclelimitGaussalgebrapolynomial