How to Solve for Primitive Roots

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Solving for primitive roots will require you to call your prime number "P" for easy reference. Solve for primitive roots with help from an experienced math professional in this free video clip.

Part of the Video Series: Solving Math Problems
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Video Transcript

Hi I'm Ryan Ault. I'm a physicist and this is how to solve for primitive roots. The first thing we should do is examine our prime number. We can call our prime number P and after we identify our prime number we can look at an equation, 2 to the N mod P. In this example we've chosen 2 as our primitive root so we are checking to see if 2 is a primitive root of the prime number P and what we have to do is look at this equation, 4, N is equal to 1 to N equal to 2 minus 1. Once we iterate through all these possible values we look to see if the outcome is unique and between 1 and P minus 1. As an example we can choose a prime number with P being equal to 3 and we can search for primitive roots of 2. So we find that 2 to the 1 mod 3 is equal to 2 and 2 to the 2 mod 3 is simply equal to 1. So we find that each outcome is unique and it's in the range from 1 to 2 so we find that 2 is a primitive root of 3. I'm Ryan Ault and this is how to solve for primitive roots.


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