# primitive roots of 17

You're asking why 2 isn't also a primitive root? that makes sense. 2: 2,4,8,5,10,9,7,3,6,1 so 2 is a primitive root. 2 8 is congruent to 1 mod 17. Their product 970377408 ≡ 1 (mod 31) and their sum 123 ≡ –1 (mod 31). Something like, oh I don't know, http://www.reddit.com/r/cheatatmathhomework. If only we and a subreddit for that. Modulo 11. Primitive Root Calculator-- Enter p (must be prime)-- Enter b . 216 = 12 + 17*12, so 216 is congruent to 12 mod 17. 0 0. leister. crumunch beat me to the punch, but I'll add that saying "the" primitive root is very much the wrong way to think about it. You're asking why 2 isn't also a primitive root? 4 years ago. 11 has phi(10) = 4 primitive roots. These are 8,7,and6 . Enter a prime number into the box, then click "submit." Smallest magnitude primitive root is the primitive root with the smallest absolute value. It follows immediately that (1) is a complete listing of the primitive roots of 17. i know 316 = 1 mod 17, but isn't 216 = 1 mod 17 as well? Their product 970377408 ≡ 1 (mod 31) and their sum 123 ≡ –1 (mod 31). 3×11 = 33 ≡ 2 12×13 = 156 ≡ 1 (–14)×(–10) = 140 ≡ 16 (–9)×(–7) = 63 ≡ 1, and 2×1×16×1 = 32 ≡ 1 (mod 31). am i missing something? Finding primitive roots . The primitive roots are 3, 10, 5, 11, 14, 7, 12, and 6. Example 1. For it to be a primitive root of p, it's required that the smallest value of h such that 2h is congruent to 1 mod p be p - 1. oh, it's because 28 hits 1 before 216 can. For example, if n = 14 then the elements of Z n are the congruence classes {1, 3, 5, 9, 11, 13}; there are φ(14) = 6 of them. Start Here; Our Story; Hire a Tutor; Upgrade to Math Mastery. When primitive roots exist mod n, (see my blog post here for a breakdown of when they do or do not exist) there will be exactly φ(φ(n)) of them. Although there can be multiple primitive root for a prime number but we are only concerned for smallest one.If you want to find all roots then continue the process till p-1 instead of breaking up on finding first primitive root. φ(φ(17)) = φ(16) = 8, so there are 8 primitive roots. Email: donsevcik@gmail.com Tel: 800-234-2933; the others are in positions whose position. Press question mark to learn the rest of the keyboard shortcuts. Menu. The primitive roots are 3, 11, 12, 13, 17 ≡ –14, 21 ≡ –10, 22 ≡ –9, and 24 ≡ –7. thanks! i'm working on some number theory homework and i didn't know who else to ask since it's late at night. Then it turns out for any integer relatively prime to 59-1, let's call it b, then \$2^b (mod 59)\$ is also a primitive root of 59. Source(s): https://shorte.im/bagFW. Primitive Root Calculator. You must have made a mistake in your arithmetic. 28 is congruent to 1 mod 17. 4- If it is 1 then 'i' is not a primitive root of n. 5- If it is never 1 then return i;. Correct me if I'm misinterpreting your question. Thus the powers of 2 from 1 to 16 won't form the desired complete reduced residue class. thanks! i didn't know there was one. The primitive roots are 3, 11, 12, 13, 17 ≡ –14, 21 ≡ –10, 22 ≡ –9, and 24 ≡ –7. The number of primitive roots modulo , if the multiplicative group is cyclic, ... 17 : 8 : 3,-3 : 3 : 3,5,6,7,10,11,12,14 Relation with other properties Smallests. Alternate Solution : Observing φ(17) = 16, if a is reduced modulo 17 then ord17 a ∈ {1,2,4,8,16}. (you can find all of them by taking odd powers of 3, if you want). Lv 4. Other related properties. so the primitive roots are 2,6,7,8. Smallest primitive root is the smallest positive number that is a primitive root modulo a given number. Finding Other Primitive Roots (mod p) Suppose that we have a primitive root, g. For example, 2 is a primitive root of 59. Let's test. i know, the homework problem was to find all 8, but i was just wondering why 2 didn't work. Primitive Roots Calculator. 2^16 = 65536 which is congruent to 1 mod(17) Which means it should be a primitive root of 17. For it to be a primitive root of p, it's required that the smallest value of h such that 2 h is congruent to 1 mod p be p - 1. 4 years ago. 3 0. hisamuddin. The first 10,000 primes, if you need some inspiration. Answer #2 | 19/04 2015 19:12 In answering an earlier question, I showed that 3 is a primitive root of 17. http://www.reddit.com/r/cheatatmathhomework. i guess it copied incorrectly, it was supposed to say 316 and 216, i'll go fix that, New comments cannot be posted and votes cannot be cast, Press J to jump to the feed. Primitive Root Video. Thus the powers of 2 from 1 to 16 won't form the desired complete reduced residue class. By using our Services or clicking I agree, you agree to our use of cookies. Primitive Root Calculator. I have plugged through the definition of the primitive root of 17, Phi(17) = 16. It will calculate the primitive roots of your number. 3×11 = 33 ≡ 2 Lv 4. definitely will use that in the future. Here is a table of their powers modulo 14: Given that 2 is a primitive root of 59, find 17 other primitive roots … Cookies help us deliver our Services. numbers are prime to 10. incongruent primitive roots of 17.

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