Show that Phi_n(x) is reducible if n is not prime.


For this one I modified the corollary for Eisenstein's Criterion to show that n divides all of the coefficients.


I used Eisenstein's Criterion with n=p^2, so that n is composite. So p divides all coefficients, and p^2 divides the last coefficient. This implies polynomial is reducible when p is not prime.

-Ozgur

Alumni Liaison

Ph.D. on Applied Mathematics in Aug 2007. Involved on applications of image super-resolution to electron microscopy

Francisco Blanco-Silva