is there an easy way to find primitive roots for a specific mod?

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- Feb 17th 2009, 02:50 PMmathisthebestpuzzlefind primitive roots for mod
is there an easy way to find primitive roots for a specific mod?

- Feb 17th 2009, 03:25 PMo_O
There isn't a specific formula to find primitive roots. However, say that you have found one primitive root, modulo . Then, is also a primitive root

**iff**and this gives the complete list.

More here: How to find a primitive root of N - Feb 17th 2009, 03:31 PMmathisthebestpuzzle
So say I have found a primitive root mod 29. namely 2.

then the other primitive roots mod 29 are powers of 2?

that means that 8 is also a primitive root because 2^3=8 and (28,3)=1.

but 2^5=32 (28,5)=1 does that mean that 3 is a primitive root because 32 mod 29 is congruent to 3?

is the only other primitive root for 29 8? - Feb 17th 2009, 03:51 PMo_O
Yes. is a primitive root mod 29

**iff**.

So for example, is a primitive root since - Feb 17th 2009, 04:03 PMmathisthebestpuzzle
but that is the only other p.r. besides 2. correct?

- Feb 17th 2009, 04:55 PMo_O
No ... there are many other values for such that .

Try

In general, every prime has primitive roots.