refer to brent's algorithm

notebooks/problem0003.ipynb

@@ -57,7 +57,7 @@
     "\n",
     "This all means that we simply need to iterate through terms in $\\{x_i\\}$ until we find $x_j$ and $x_k$ such that $\\gcd(x_j - x_k, n)$ equals something other than 1. When it does, by definition this will be a factor of $n$. However, this factor may be $n$ itself, which is trivial. In this case the algorithm fails, but it can be attempted again with a different value for $x_0$.\n",
     "\n",
-    "To facilitate finding $x_j$ and $x_k$, [Floyd's cycle-finding algorithm](https://en.wikipedia.org/wiki/Cycle_detection) is used. Briefly, two variables are used to iterate through $\\{x_i\\}$ at different rates. Because of this, the two variables will never have the same index, but eventually $x_i \\equiv x_j \\pmod{p}$, which we will detect with the GCD."
+    "To facilitate finding $x_j$ and $x_k$, [Brent's cycle-finding algorithm](https://en.wikipedia.org/wiki/Cycle_detection) is used. Briefly, two variables are used to iterate through $\\{x_i\\}$ at different rates. Because of this, the two variables will never have the same index, but eventually $x_i \\equiv x_j \\pmod{p}$, which we will detect with the GCD."
    ]
   },
   {