- #1

chwala

Gold Member

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- 286

- Homework Statement:
- See attached

- Relevant Equations:
- Ring Theory

My interest is on the highlighted; my understanding is that,

let

##f(x)=x^3+x^2+2^{'}##

then

##f(1^{'})=1{'}+1{'}+2^{'}=4^{'} ##

we know that in ##\mathbb{z_3} ## that ##\dfrac{4}{3}=1^{'}##

##f(2^{'})=8^{'}+4^{'}+2^{'}=14{'} ##

we know that in ##\dfrac{14^{'}}{3}=1^{'}##...

I hope that is the correct reasoning for the highlighted part indicated in red.