For a large prime p, and a polynomial f over a finite field Fp of p elements, we obtain a lower bound on the size of the multiplicative subgroup of Fp∗ containing H ≥ 1 consecutive values f(x), x = u +1, . . . , u + H, uniformly over f ∈ Fp[X] and an u ∈ Fp.
- polynomial congruences
- finite fields