Ramanujan-Nagell equation
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In mathematics, Ramanujan-Nagell'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 Trygve Nagell.
[edit] Triangular Mersenne numbers
The problem of finding all numbers of the form 2b - 1 (Mersenne numbers) which are triangular is closely related [1]. The answer is 0, 1, 3, 15, 4095 and no more (sequence A076046 in OEIS).
