• Nov 27th 2012, 07:53 AM
babygill
Let p be a prime number with p>3. Prove that the sum of the quadratic residues modulo p is divisible by p.
• Nov 27th 2012, 01:04 PM
topsquark
Quote:

Originally Posted by babygill
Let p be a prime number with p>3. Prove that the sum of the quadratic residues modulo p is divisible by p.

How far have you gotten with this?

-Dan
• Nov 27th 2012, 01:31 PM
babygill
I don't know where to start
• Nov 27th 2012, 04:25 PM
topsquark
For example, take a look at the multiplicative group mod 7: $\mathBB{Z} / _7 \mathbb{Z} = \{ 1, 2, 3, 4, 5, 6 \}$.
$\sum_{i = 1}^6~i^2$