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Show that Phi_n(x) is reducible if n is not prime. | Show that Phi_n(x) is reducible if n is not prime. | ||
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| + | For this one I modified the corollary for Eisenstein's Criterion to show that n divides all of the coefficients. | ||
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| + | 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. | ||
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| + | -Ozgur | ||
Latest revision as of 08:54, 16 November 2008
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
