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

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- Mar 21st 2010, 04:12 PMNikoBellic...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.

- Mar 21st 2010, 04:49 PMchiph588@
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.