Proposed by Marian Tetiva, National College "Gheorghe Rosca Codreanu," Birlad, Romania. Let P be a polynomial of degree n with complex coefficients and with p(0) = 0. Show that for any complex alfa with alfa <1 there exist complex numbers Z1, .... , Zn+2, all of norm 1, such that P(a) = P(z1) + ... + P(Zn+2).
|Journal||American Mathematical Monthly|
|Publication status||Published - 2011|