`B = (p, r)`

Enter a value for all fields

The Primitive Roots equation calculates whether a given number is a primitive root of a given parent number. 

INSTRUCTIONS: Enter the following

• (p) Parent Number
• (r) Suspected Root Number

Result (B): The result will tell you whether r is or is not a primitive root of p

The Math / Science

Is 2 a primitive root of 11?

• p = 11
• r = 2

1. List out all the numbers from 1 to p - 1 
   • ​​​​​​​​​​​​​​11 - 1 = 10​​​​​​​
2. Raise r to the powers of 1 and take the result of that mod p
   • ​​​​​​​2¹ mod 11 = 2
3. Repeat this step for the rest of the values up to 10
   • 2² mod 11 = 4
   • 2³ mod 11 = 8
   • 2⁴ mod 11 = 5
   • 2⁵ mod 11 = 10
   • 2⁶ mod 11 = 9
   • 2⁷ mod 11 = 7
   • 2⁸ mod 11 = 3
   • 2⁹ mod 11 = 6
   • 2¹⁰ mod 11 = 1
4. If all results are distinct (no repeating numbers) then 2 is a primitive root of 11