Show that if g and h are primitive roots of an odd prime p, then their product gh is not a primitive root of p.

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- Mar 24th 2010, 09:18 AMtarheelbornPrimitive Roots
Show that if g and h are primitive roots of an odd prime p, then their product gh is not a primitive root of p.

- Mar 24th 2010, 10:16 AMtonio
- Mar 24th 2010, 12:16 PMBruno J.
That is not true. For instance is certainly not a primitive root for any prime , but for primes of the form ...

What you mean is that*if*is a primtive root then , i.e. if is a primitive root then it's not a quadratic residue. Since the product of two nonresidues is a residue... - Mar 24th 2010, 12:27 PMtarheelborn
I am sorry, but I am not following you. Can you please elaborate?

- Mar 24th 2010, 12:38 PMBruno J.
If are primitive roots, then , and , therefore is not a primitive root.

- Mar 24th 2010, 01:15 PMtonio