On Fully Split Lacunary Polynomials in Finite Fields
Khodakhast Bibak, Igor E. Shparlinski · Bulletin of the Polish Academy of Sciences Mathematics · 2011
We estimate the number of possible degree patterns of $k$-lacunary polynomials of degree $t < p$ which split completely modulo $p$. The result is based on a combination of a bound on the number of zeros of lacunary polynomials with some graph theory