Recent content by jacquelinek

Give one primitive element for each of the finite field: F2n (here "2" is the subscript) for n=1, n=2,...,n=8

Prove that: g is a generator of Fp* if and only if g^(p-1) = 1 (mod p) and gq ≠ 1 (mod p) for all prime divisors q of (p – 1). I am thinking about applying Fermat's theorem...but don't know how... Request help, thanks.

I know that if n is odd and has k distinct prime factors, then the number of roots, x^2 = 1 (mod n), is equal to 2^k. However, I don't know how to give a formal proof to it. I simply want to bypass the generalized form x^2 = a (mod n). How can I prove it directly? Thank you.