Question

Let b be a primitive root for the odd prime p. Prove that b^k is a...

Let b be a primitive root for the odd prime p. Prove that b^k is a primitive root for p if and only if gcd(k, p − 1) = 1.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let p be a prime and let a be a primitive root modulo p. Show that...
Let p be a prime and let a be a primitive root modulo p. Show that if gcd (k, p-1) = 1, then b≡ak (mod p) is also a primitive root modulo p.
Use the fact that each prime possesses a primitive root to prove Wilson’s theorem: If p...
Use the fact that each prime possesses a primitive root to prove Wilson’s theorem: If p is a prime, then (p−1)! ≡ −1 (mod p).
Let p be an odd prime and let a be an odd integer with p not...
Let p be an odd prime and let a be an odd integer with p not divisible by a. Suppose that p = 4a + n2 for some integer n. Prove that the Legendre symbol (a/p) equals 1.
Let p be an odd prime. Prove that −1 is a quadratic residue modulo p if...
Let p be an odd prime. Prove that −1 is a quadratic residue modulo p if p ≡ 1 (mod 4), and −1 is a quadratic nonresidue modulo p if p ≡ 3 (mod 4).
Let p be an odd prime. Let f(x) ∈ Q(x) be an irreducible polynomial of degree...
Let p be an odd prime. Let f(x) ∈ Q(x) be an irreducible polynomial of degree p whose Galois group is the dihedral group D_2p of a regular p-gon. Prove that f (x) has either all real roots or precisely one real root.
Let m > 1. If there exists a primitive root modulo m, prove that there are...
Let m > 1. If there exists a primitive root modulo m, prove that there are exactly φ(φ(m)) primitive roots modulo m. *Note that φ() is Euler's totient function.
Let p be an odd prime, and let x = [(p−1)/2]!. Prove that x^2 ≡ (−1)^(p+1)/2...
Let p be an odd prime, and let x = [(p−1)/2]!. Prove that x^2 ≡ (−1)^(p+1)/2 (mod p). (You will need Wilson’s theorem, (p−1)! ≡−1 (mod p).) This gives another proof that if p ≡ 1 (mod 4), then x^2 ≡ −1 (mod p) has a solution.
Formal Proof: Let p be a prime and let a be an integer. Assume p ∤...
Formal Proof: Let p be a prime and let a be an integer. Assume p ∤ a. Prove gcd(a, p) = 1.
Prove: Let (a,b,c) be a primitive pythagorean triple. then we have the following 1. gcd(c-b, c+b)...
Prove: Let (a,b,c) be a primitive pythagorean triple. then we have the following 1. gcd(c-b, c+b) =1 2. c-b and c+b are squares
1. Prove that {2k+1: k ∈ Z}={2k+3 : k ∈ Z} 2. Prove/disprove: if p and...
1. Prove that {2k+1: k ∈ Z}={2k+3 : k ∈ Z} 2. Prove/disprove: if p and q are prime numbers and p < q, then 2p + q^2 is odd (Hint: all prime numbers greater than 2 are odd)
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT