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 for Goldbach’s Conjecture (Two Primes with given Sum)
- Program to implement Collatz Conjecture
- Removing a number from array without changing its arithmetic mean
- Remove minimum elements from the array such that 2*min becomes more than max
- Number of balanced parenthesis substrings
- Check whether the triangle is valid or not if angles are given
- Append a digit in the end to make the number equal to the length of the remaining string
- Alternate XOR operations on sorted array
- Sum of the Tan(x) expansion upto N terms
- Perimeter of an Ellipse
- Maximum value after merging all elements in the array
- Program to Find the Incenter of a Triangle
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