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

Here's a revised version of my previous conjecture, but with a
substantially scaled down, more realistic claim ...

Conjecture:

Let p be prime, and let q be a prime factor of p - 1.

If f in Z_p[x], regarded as a function from Z_p to Z_p, is such that

(1) deg(f) = q

(2) For all a in Z_p, f(a) = b^q for some b in Z_p

then f = g^q for some g in Z_p[x] with deg(g) = 1.

quasi
.