Definition:Ramanujan-Nagell Equation

Definition

The Ramanujan-Nagell equation is the Diophantine equation:

$x^2 + 7 = 2^n$

Also known as

The Ramanujan-Nagell equation is also known as Ramanujan's equation and Ramanujan's square equation.

Source of Name

This entry was named for Srinivasa Ramanujan and Trygve Nagell.

Historical Note

Srinivasa Ramanujan conjectured in $1913$ that the equation $x^2 + 7 = 2^n$ had only $5$ integer solutions.

The same conjecture was made independently in $1943$ by Wilhelm Ljunggren.

The conjecture was proved in $1948$ by Trygve Nagell