Exceptional scatteredness in prime degree

Let q be an odd prime power and n an integer. Let ℓ∈Fq(n) be a q-linearized t-scattered polynomial of linearized degree r. Let d=max⁡{t,r} be an odd prime number. In this paper we show that under these assumptions it follows that ℓ=x. Our technique involves a Galois theoretical characterization of t-scattered polynomials combined with the classification of transitive subgroups of the general linear group over the finite field Fq.