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10/28/2008
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10/14/2008
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09/09/2008
08/26/2008
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07/29/2008
07/22/2008
07/15/2008
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02/26/2008
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01/15/2008
01/08/2008
12/04/2007
11/27/2007
11/20/2007
11/13/2007
11/06/2007
10/30/2007
10/16/2007

November 13–November 19, 2007

Problem

Show that for all natural numbers k, the function

f(x) = x^4k - x^2k+1 + x^2k - x + 1

is positive for all real numbers x.

Solution

List of solvers

Aaron Dilley (undergraduate); Field Cady, Dustin Moody, Jacob Lewis, Gary Raymond (graduate); Rich Bauer (alum)

Aaron Dilley wins the prize!