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PROBLEMS AND SOLUTIONS Edited by Gerald A. Edgar, Doug Hensley, Douglas B. West

Edited by Gerald A. Edgar, Doug Hensley, Douglas B. West
with the collaboration of Mario Benedicty, Itshak Borosh, Paul Bracken, Ezra A.
Brown, Randall Dougherty, Tam´as Erd´elyi, Zachary Franco, Christian Friesen, Ira M.
Gessel, L´aszl´o Lipt´ak, Frederick W. Luttmann, Vania Mascioni, Frank B. Miles, Bog-
dan Petrenko, Richard Pfiefer, Cecil C. Rousseau, Leonard Smiley, Kenneth Stolarsky,
Richard Stong, Walter Stromquist, Daniel Ullman, Charles Vanden Eynden, Sam Van-
dervelde, and Fuzhen Zhang.
Proposed problems and solutions should be sent in duplicate to the MONTHLY
problems address on the inside front cover. Submitted solutions should arrive at
that address before September 30, 2009. Additional information, such as gen-
eralizations and references, is welcome. The problem number and the solver's
name and address should appear on each solution. An asterisk (*) after the num-
ber of a problem or a part of a problem indicates that no solution is currently
11432. Proposed by Marian Tetiva, National College "Gheorghe Ros¸ca Codreanu,"
B^irlad, Romania. Let P be a polynomial of degree n with complex coefficients and
with P(0) = 0. Show that for any complex with || < 1 there exist complex num-
bers z1, . . . , zn+2, all of norm 1, such that P() = P(z1) + ˇ ˇ ˇ + P(zn+2).


Source: Alekseyev, Max - Department of Computer Science and Engineering, University of South Carolina


Collections: Biotechnology; Computer Technologies and Information Sciences