Super Magic Box

Put in a value for D to compute its Super Magic Box:

n

A_{n} = a_{n - 1} C_{n - 1} - A_{n - 1}

C_{n} = (D - A_{n}^{2}) / C_{n - 1}

a_{n} = ⌊ (A_{n} + a_{0}) / C_{n} ⌋

p_{n} = a_{n} p_{n - 1} + p_{n - 2}

q_{n} = a_{n} q_{n - 1} + q_{n - 2}

p_{n}^{2} - D q_{n}^{2}

The fundamental unit in $ℤ [\sqrt{D}]$ is $a + b \sqrt{D}$ , with norm $N$

A factorization of $D$ is given by $\gcd (p + C, D) = d \to D = d * (p + C)$