Let P 1 ; . . . ; P m ∈ Z[y] be any linearly independent polynomials with zero constant term. We show that there exists γ > 0 such that any subset of F q of size at least q 1-γ contains a nontrivial polynomial progression x,x+P 1 (y); . . . . x+P m (y) provided that the characteristic of F q is large enough.
All Science Journal Classification (ASJC) codes