Ramanujan's Square Equation

It has been proved that the only solutions to the Diophantine Equation

$$2^n-7=x^2$$

are $n=3$, 4, 5, 7, and 15 (Beeler et al. 1972, Item 31).

References

Beeler, M.; Gosper, R. W.; and Schroeppel, R. HAKMEM. Cambridge, MA: MIT Artificial Intelligence Laboratory, Memo AIM-239, Feb. 1972.