# stuck on a proof of x^n congr. 1 mod p

• April 4th 2009, 05:09 PM
minivan15
stuck on a proof of x^n congr. 1 mod p
assumptions: p is a prime number.

1<= a <= (p-1)

the order of a modulo p is d

d| (p-1)

describe the solutions of the congruence x^d congr. 1 (mod p) in terms of a. Does this give all the solutions of x^d congr. 1 (mod p) ?

I'm really blanking for some reason... obviously any power of a works but...where to go from there?
• April 5th 2009, 03:00 PM
ThePerfectHacker
Quote:

Originally Posted by minivan15
assumptions: p is a prime number.

1<= a <= (p-1)

the order of a modulo p is d

d| (p-1)

describe the solutions of the congruence x^d congr. 1 (mod p) in terms of a. Does this give all the solutions of x^d congr. 1 (mod p) ?

The solutions are $1,a,a^2,...,a^{d-1}$.