- #1
Mathsgirl
- 5
- 0
Homework Statement
Hi,
I can't figure out this problem:
Let a in Zn be a unit. Show that (X+a)n - (Xn + a) = 0 in Zn[X] if and only if n is prime.
Thanks for any help :)
Homework Equations
Binomial expansion
The Attempt at a Solution
There is a hint which says to show that if n is not prime then n doesn't divide nCp if p is a prime divisor of n. I'm not sure how to show this or how to use it in the main proof.
If I assume the LHS is true I can expand it using the binomial expansion but I don't seem to get anything useful. I can factorise out an a.