Solutions of Ramanujan-Nagell Equation

Theorem
Integer solutions to the Ramanujan-Nagell equation:
 * $x^2 + 7 = 2^n$

exist for only $5$ values of $n$:


 * $3, 4, 5, 7, 15$

The corresponding values of $x$ are:
 * $1, 3, 5, 11, 181$

Proof
By direct implementation:

Also see

 * Five Ramanujan-Nagell Numbers