|Oct20-10, 12:36 PM||#1|
Zn[X] and primality
1. The problem statement, all variables and given/known data
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 :)
2. Relevant equations
3. 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.
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