A primitive normal pair with prescribed prenorm

For any positive integers q, n, m with q being a prime power and n ≥ 5, we establish a condition sufficient to ensure the existence of a primitive normal pair (ε,f(ε)) in F_qⁿ over Fq such that PNqⁿ/q(ε)=a, where aq is prescribed. Here f=f₁/f₂qⁿ(x) is a rational function subject to some minor restrictions such that deg(f₁)+deg(f₂)$=m$ and PNqⁿ/q(ε) =∑ᵢ₌₀ⁿ⁻¹(j≠ i0≤ j≤ n-1∏_^εqʲ). Finally, we conclude that for $m=3$, n≥ 6, and q=7ᵏ where k, such a pair will exist certainly for all $(q,n)$ except possibly $10$ choices at most.