Let be an odd prime.
A primitive root mod is an integer with the order of
I have shown
(This is the Legendre symbol)
Here is the question:
Using primitive roots show there are the same number of quadratic residues as there are quadratic nonresidues modulo
I am aware of the "standard" proof of this result which uses Lagrange's theorem (for polynomials) but I don't know how to prove it using primitive roots.
Obviously since then any primitive root is a quadratic non residue but this is as far as I have got.
I tried to use Euler's criterion somehow but couldn't see a way forward.
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- Thread Starter
- 12-01-2017 19:09
- 12-01-2017 20:56