From cba16eb5d1afc2bdf854974e7da499814f3b21a0 Mon Sep 17 00:00:00 2001 From: filifa Date: Sun, 11 May 2025 23:08:30 -0400 Subject: [PATCH] refer to brent's algorithm --- notebooks/problem0003.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/notebooks/problem0003.ipynb b/notebooks/problem0003.ipynb index b4cadf3..1c2e8c4 100644 --- a/notebooks/problem0003.ipynb +++ b/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." ] }, {