Given a prime power q and positive integer n, let Fqn denote the finite field with qn elements. Also a,b be arbitrary members of ground Fq. We investigate existence non-zero element ξ∈Fqn such that ξ+ξ−1 is primitive T(ξ)=a, T(ξ−1)=b, where T(ξ) denotes trace ξ in This was question intended to addressed by Cao Wang (2014). Their work dealt instead another problem already literature. Our solutio...