The no-solution conjecture for the plus exponential Diophantine equation

Let $a,b,n,x$ be positive integers with $a<b$, and consider

$$(a^n+1)(b^n+1)=x^2.$$

No-solution conjecture for the plus equation. This equation has no solutions in positive integers for $n\geq4$. The conjecture is proposed as an analogue of Cohn's conjectures for the minus equation. The paper gives computational and theoretical motivation, but no resolution is stated.