Ramanujan-Nagell equation

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In mathematics, Ramanujan-Skolem's theorem is the solution of a particular exponential Diophantine equation.

Given the equation

2ⁿ − 7 = x²

solutions in natural numbers n and x exist only when

n = 3, 4, 5, 7 and 15.

This was conjectured by Srinivasa Ramanujan, and proved by Thoralf Skolem.