What is the primitive root of 17?

What is the primitive root of 17?

Table of primitive roots

	primitive roots modulo	order (OEIS: A000010)
17	3, 5, 6, 7, 10, 11, 12, 14	16
18	5, 11	6
19	2, 3, 10, 13, 14, 15	18
20		8

How do you find the primitive roots?

A primitive root mod n is an integer g such that every integer relatively prime to n is congruent to a power of g mod n. That is, the integer g is a primitive root (mod n) if for every number a relatively prime to n there is an integer z such that. a \equiv \big(g^z \pmod{n}\big). a≡(gz(modn)).

What is a primitive root of 13?

Primitive Root

7	3, 5
9	2, 5
10	3, 7
11	2, 6, 7, 8
13	2, 6, 7, 11

How do you find the primitive root of 19?

So, if at all 2 has order k modulo 19, and then the possible values of k are 1,2,3,6, and 9. From this, we follow that 18 is the smallest positive integer such that . 2 is a primitive root of 19.

Do all prime numbers have primitive roots?

Every prime number has a primitive root. Let p be a prime and let m be a positive integer such that p−1=mk for some integer k.

Does 20 have primitive roots?

Since φ(20) = φ(4)φ(5) = 2·4 = 8, it follows immediately that 20 has no primitive root.

How many primitive roots are there?

The number of primitive roots mod p is ϕ(p−1). For example, consider the case p = 13 in the table. ϕ(p−1) = ϕ(12) = ϕ(223) = 12(1−1/2)(1−1/3) = 4. If b is a primitive root mod 13, then the complete set of primitive roots is {b1, b5, b7, b11}.

Does 15 have primitive roots?

Show that there is no primitive root mod 15. so all possible r have ord15r < 8 and no primitive roots exist. 4.

How do you find the primitive root of 343?

The cube root of 343 = 7. Hence, 7+15 = 22. 4.

How many primitive roots are there for 19?

Explanation: 2, 3, 10, 13, 14, 15 are the primitive roots of 19.