Prove that 2 is a primitive root modulo 11 ^ k for every integer k >= 1
Added by Melissa S.
Step 1
A number g is called a primitive root modulo n if for every integer a coprime to n, there is an integer k such that g^k ≡ a (mod n). In other words, the powers of g generate all the numbers coprime to n. Now, we need to prove that 2 is a primitive root modulo Show more…
Show all steps
Close
Your feedback will help us improve your experience
Nick Johnson and 53 other Algebra educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Show that 2 is a primitive root mod 11, and then, find all primitive roots mod 11.
Shamshad N.
Let r be a primitive root mod p and let k be a positive integer (p > 2). Show that r^k is a quadratic residue mod p if and only if k is even.
Madhur L.
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.
Sri K.
Recommended Textbooks
Elementary and Intermediate Algebra
Algebra and Trigonometry
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD