David, Yes, it is true and well-known. It's more usually written in the form: if p = 3 mod 4, then h(-p) = -(1/p) sum_{m=1}^{p-1} m (m/p), where (m/p) is the Legendre symbol (qudratic residue symbol). For example, see "Multiplicative Number Theory" by Davenport, page 53 (first edition). Victor On Mon, Mar 15, 2010 at 7:23 PM, David Wilson <davidwwilson@comcast.net> wrote:
Let f(n) = SUM(0 <= k < n; (k^2) mod n)
where mod is the remainder function.
It looks as if, for prime p >= 5
f(p) =
1 if p == 1 (mod 4) 2c+1 if p == 3 (mod 4)
where c is the class number of Q(sqrt(-p))
Is this true? Well known?
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun