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
- Triangle of numbers arising from Gilbreath's conjecture
- Check if the sum of digits of number is divisible by all of its digits
- Program for Mobius Function | Set 2
- Make the list non-decreasing by changing only one digit of the elements
- Maximum items that can be bought with the given type of coins
- Count occurrences of a prime number in the prime factorization of every element from the given range
- Check if the number is valid when flipped upside down
- Find the count of subsequences where each element is divisible by K
- Count of numbers below N whose sum of prime divisors is K
- Queries for the smallest and the largest prime number of given digit
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