Theorem: If p is a prime, then there is a primitive root for p. We will find the primitive roots of 11. Relevance. 11 has phi(10) = 4 primitive roots. User #102722 2872 posts. Whirlpool Forums Addict reference: whrl.pl/Rbqyok. These are 8,7,and6. Let's test. the others are in positions whose position . 2: 2,4,8,5,10,9,7,3,6,1 so 2 is a primitive root. Since F(F(11)) = F(10) = 4, we know that 11 has four primitive roots, and they are 2, … We know that $\phi (7) = 6$.Hence any of the least residues (mod 7) with order 6 are primitive roots. Question: Find All Primitive Roots Mod 11. This link describes a fairly straightforward way to find primitive roots. Cyclotomic Polynomials. 1, 2, 4, 8, 3, 6, 12, 11, 9, 5, 10, 7---which is all of the classes mod 13 except 0. Expert Answer . First, recall an important theorem about primitive roots of odd primes: Let F denote the Euler phi function; if p is an odd prime, then p has F(F(p)) = F(p-1) primitive roots. MHF Hall of Fame. 5, 1 0, 3, 8, 1, 6, 1 1, 4, 9, 2, 7, 0, 5, 1 0, …. T. ThePerfectHacker. MaxReboBand. There are other primitive roots for 13. 4 Answers. 1 decade ago. 5, 10, 3, 8, 1, 6, 11, 4, 9, 2, 7, 0, 5, 10, …. knashha. See the answer. Answer Save. ref: whrl.pl/Rbqyok. Find all primitive roots mod 11. Thanks . Example: If p=13, then 2 is a primitive root because the powers of 2 are. You can help me ? My teacher said that "if p is primitive root of N ,or p or p+N is primitive root of N^2 " but he didn't said the general primitive root of 11^2. find the primitive root of 11^2 if we know 2,3 is primitive root of 11. numbers are prime to 10. This problem has been solved! 5,10,3,8,1,6,11,4,9,2,7,0, \, 5,10,\ldots. Previous question Next question Get more help from Chegg. posted 2008-Feb-8, 6:24 pm AEST edited 2008-Feb-8, 7:12 pm AEST. Not sure if it's the fastest around, but it's certainly the simplest to understand. Favourite answer. Every element in Z / 12 {\mathbb Z}/12 Z / 1 2 is on that list. Lv 5. Even if I find one primitive root modulo 11, how would I find out how many the prime 11 has in total?
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