Ramanujan–Nagell equation

The Ramanujan–Nagell equation is a famous equation in number theory given by: \[ 2^n = x^2 + 7 \] where \(n\) is a non-negative integer and \(x\) is an integer. The equation states that \(2^n\) can be expressed as the sum of a perfect square \(x^2\) and the integer 7. The equation is considered particularly interesting because it leads to a list of specific solutions.