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Old 2017-04-07, 00:35   #1
carpetpool
 
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"Sam"
Nov 2016

2·163 Posts
Post Polynomial whose coefficients add up to n defining Cyclotomic field K.

Let n be an integer defining the cyclotomic properties of K (meaning that n is a factor of the cyclotomic polynomial C_K(x) evaluated at some x value). How many polynomials P(x), the same degree as C_K(x) their coefficients add up to n? For instance, choosing the cyclotomic field 3, C_3(x) = x^2+x+1, and x = 7, 19 is a factor of 7^2+7+1. How many polynomials P(x) of the form ax^2+bx+c defining the same field as x^2+x+1 is it the case that a+b+c = 19 where a, b, c are integers -19 <= (a, b, c) <= 19? Thanks for help, comments, and clarification.

Last fiddled with by carpetpool on 2017-04-07 at 00:35
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