On an open problem of Niederreiter

Niederreiter in 1991 proposed an open problem–to characterize the polynomials in Fq[x1,…,xn] which are permutation polynomials over every finite extension of Fq. The answer is well known for the case n=1. In this paper the author studies it for the case n=2 and solves the problem under a condition gcd and Deg f 0 (mod p)