Solution of Ljunggren Equation

Theorem
The only solutions of the Ljunggren equation:
 * $x^2 + 1 = 2 y^4$

are:
 * $x = 1, y = 1$
 * $x = 239, y = 13$

Proof
Setting $x = 1$:

and so $y = 1$.

Setting $x = 239$:

and so $y = 13$.

Also see

 * Largest Prime Factor of $n^2 + 1$