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
- Program to implement Collatz Conjecture
- Program for Goldbach’s Conjecture (Two Primes with given Sum)
- Maximum Sequence Length | Collatz Conjecture
- Triangle of numbers arising from Gilbreath's conjecture
- Multiply Large Numbers using Grid Method
- Maximum frequency of a remainder modulo 2i
- Sum of the updated array after performing the given operation
- Remove an element to minimize the LCM of the given array
- Find closest integer with the same weight
- Check whether the given decoded string is divisible by 6
- Find the minimum possible health of the winning player
- Construct an array from its pair-product
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.