Ma's second conjecture on a quadratic exponential equation

Let $p$ be an odd prime, $a\in\mathbb{Z}$ with $a\geq0$, and $x,m,n\in\mathbb{N}$. Ma's second conjecture. The equation

$$x^2=2^{2a+2}p^{2n}-2^{a+2}p^{m+n}+1$$

has only the solution $(p,x,a,m,n)=(5,49,3,2,1)$. The source gives no resolution of this conjecture.