Online Course Discussion Forum

返回至:站点

Math Challenge III 2.7

 
 
ShiJames的头像
Math Challenge III 2.7
ShiJames - 2020年07月8日 Wednesday 20:14
 

For this problem, I decided to factor out a z^(3m) and get z^3m (z^2 + z + 1) - z^3m + 1. The first part is divisible by z^2 + z + 1, so I need to prove that 1 - z^3m is also divisible by z^2 + z + 1. Factoring, I got (1 - z^m)(z^2m + z^m + 1). This is similar to z^2 + z + 1, but I do not know what to do now. Is this a bad strategy? Is there a better way to approach this problem? Thank you.

 
WangDr. Kevin的头像
Re: Math Challenge III 2.7
WangDr. Kevin - 2020年07月9日 Thursday 00:23
 

The Polynomial Factor theorem says: a polynomial $P(z)$ has a factor $(z-a)$ if and only if $P(a)=0$.  Here you can let $a=\omega$ and $a=\omega^2$.

 
显示父帖