Perform the Indicated operation (x+1)^3 in Z3[x]
\[ (x+1)^{3} in Z_{3}[x]\]
\[\huge (x+1)^3 \ \ \ \ in \ \mathbb{Z}_3[x]\] LOL any idea how to do this? :)
do i just use f(0) and f(1) to solve for them in Z3? I'm not sure really thats why I'm asking and my book doesn't even address it.
hint \(3\equiv 0\)
Freshman's dream :D Anyway, evaluate this (x+1)^3 normally first, and tell me what you get.
lol
Cube of a binomial?
1+3 x+3 x^2+x^3
That's right :) \[\huge x^3 + 3x^2+3x+1\]but... we take everything in mod 3... In particular, in \[\large \mathbb{Z}_3\] 3=0, right?
yes
so is it X^3 + 1?
You got it :) And now, for any prime number p
\[\huge (a+b)^p=a^p+b^p \ \ \ \ \ in \ \mathbb{Z}_p\]
i always suspected my math teachers were lying, and \((a+b)^3=a^3+b^3\)
Oh abstract algebra... so deceptive :D That was fun... but I'm getting drowsy :/ ----------------------------------------- Terence out
Thank you
Join our real-time social learning platform and learn together with your friends!