Skip to content
Related Articles

Related Articles

Improve Article
Save Article
Like Article

Ramanujan–Nagell Conjecture

  • Last Updated : 12 Mar, 2018

The Ramanujan-Nagell equation is an equation between a number (say, x) which is squared and another number (say, z) such that z = 2^n - 7. 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 :
2^n - 7 = x^2
and solutions in natural numbers x and n exist just when n = 3, 4, 5, 7 and 15.

Some examples are 
2^3 - 7 = (\pm1)^2, where n = 3 and x = \pm1
2^4 - 7 = (\pm3)^2, where n = 4 and x = \pm3
2^5 - 7 = (\pm5)^2, where n = 5 and x = \pm5

The conjecture is quintessential to the problem of finding Triangular Mersenne numbers

My Personal Notes arrow_drop_up
Recommended Articles
Page :

Start Your Coding Journey Now!