Thread: ...sum of all quadratic residues modulo p...

Let p be a prime > 3. Show that the sum of all the quadratic residues modulo p is divisible by p.

Originally Posted by NikoBellic

Let p be a prime > 3. Show that the sum of all the quadratic residues modulo p is divisible by p.

Let be a primitive root modulo .

is the collection of all quadratic residues.
This is because and every element in is a square due to the even exponent. Since there are only quadratic residues, must be the list of quadratic residues modulo .

.

, otherwise doesn't exist.