Is 3 a primitive root of 7?
If p is prime, then b is a primitive root if
Powers of b include all residue classes mod p
Primitive Root Table:
| n | n - 1 | bn - 1 | bn - 1 mod p |
|---|---|---|---|
| 1 | 0 | 30 = 1 | 30 mod 7 = 1 |
| 2 | 1 | 31 = 3 | 31 mod 7 = 3 |
| 3 | 2 | 32 = 9 | 32 mod 7 = 2 |
| 4 | 3 | 33 = 27 | 33 mod 7 = 6 |
| 5 | 4 | 34 = 81 | 34 mod 7 = 4 |
| 6 | 5 | 35 = 243 | 35 mod 7 = 5 |
Final Evaluation:
3 is a primitive root of 7
What is the Answer?
3 is a primitive root of 7
How does the Primitive Root Calculator work?
Free Primitive Root Calculator - Given a prime number p and a potential root of b, this determines if b is a primitive root of p.
This calculator has 2 inputs.
This calculator has 2 inputs.
What 1 formula is used for the Primitive Root Calculator?
bn - 1 mod p
What 3 concepts are covered in the Primitive Root Calculator?
- modulus
- the remainder of a division, after one number is divided by another.
a mod b - prime number
- a natural number greater than 1 that is not a product of two smaller natural numbers.
- primitive root
- if every number a coprime to n is congruent to a power of g modulo n
