The Ramanujan-Nagell equation is an equation between a number (say, x) which is squared and another number (say, z) such that z = . Here, n can be any positive natural number which satisfies the equation. It is an example of an exponential Diophantine equation, which is an equation that can have only integral solutions with one of the variables (here, n) present as an exponent in the equation.
Therefore, the equation is :
and solutions in natural numbers x and n exist just when n = 3, 4, 5, 7 and 15.
Some examples are 2^3 - 7 = (1)^2, where n = 3 and x = 1 2^4 - 7 = (3)^2, where n = 4 and x = 3 2^5 - 7 = (5)^2, where n = 5 and x = 5
The conjecture is quintessential to the problem of finding Triangular Mersenne numbers
- Legendre's Conjecture
- Lemoine's Conjecture
- Goldbach's Weak Conjecture for Odd numbers
- Program for Goldbach’s Conjecture (Two Primes with given Sum)
- Program to implement Collatz Conjecture
- Maximum Sequence Length | Collatz Conjecture
- Triangle of numbers arising from Gilbreath's conjecture
- Count of pairs satisfying the given condition
- Count number of ways to cover a distance | Set 2
- Reduce a number to 1 by performing given operations | Set 2
- Minimum integer that can be obtained by swapping adjacent digits of different parity
- Jaro and Jaro-Winkler similarity
- Number of binary strings such that there is no substring of length ≥ 3
- Partitions possible such that the minimum element divides all the other elements of the partition
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