How often does the polynomial x^n-1 have a divisor of every degree between 1 and n in Z[x]? We say that such an integer n is ``phi-practical.'' In this talk, we discuss some recent results concerning the distribution of phi-practical numbers. We will also describe several related projects with student co-authors that came out of the Max Planck Institute's summer intern program. This talk includes joint work with subsets of the following co-authors: Paul Pollack, Carl Pomerance, Andreas Weingartner, Nicholas Schwab, and Leo Gitin.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/246