PERMUTAON POLYNOMIALS OF THE TYPE 1+frac{q-1}{m}} + ax$

In this paper, we prove that $x^{1+\frac{q-1}{5}} + ax (a \neq 0)$ is not a permutation polynomial over $F_{q^r} (r \geq 2)$ and we show some properties of $x^{1+\frac{q-1}{m}} + ax (a \neq 0)$ over $F_{q^r} (r \geq 2)$.