Re: math -- values of f(x) (mod p)

In article <9kttv3576lm2p6jafgbtnese9lkorpv8il@xxxxxxx>,
quasi <quasi@xxxxxxxx> wrote:

Two conjectures ...

Conjecture (1):

If n is an odd positive integer, then for all sufficiently large
primes p (depending on n), there does not exist f in Z_p[x], with
deg(f) = n, such that for all r in Z_p, f(r) is a square in Z_p.

I think this is known. I think there are estimates for
sum over x in Z_p of Legendre symbol ( f(x) / p ) of the form
constant sqrt p where constant depends on n. Maybe the textbook
by Ireland & Rosen is a good place to start.

--
Gerry Myerson (gerry@xxxxxxxxxxxxxxx) (i -> u for email)
.