Distribution of values of polynomial Fermat quotients

Let P be an irreducible polynomial of degree n   over FqFq. For A∈Fq[X]A∈Fq[X] with gcd(A,P)=1gcd(A,P)=1 the polynomial Fermat quotient qP(A)qP(A) is defined byqP(A)≡Aqn−1−1P(modP)anddegqP(A)