Generalizations of the Markoff–Hurwitz equations over finite fields Original Research Article

Let Nq be the number of solutions of the equationimage over the finite field image. L. Carlitz found formulas for Nq for n=3 and for n=4 and image. He also expressed Nq for n=4 and image in terms of Jacobsthal sums. In an earlier paper, we found formulas for Nq when d=gcd(n−2,(q−1)/2)=1 or 2. In this paper, we find formulas for Nq when d=4 and image; and when there exists an l such that image.