From 6fbee468b5a717b0e7e3bc46c06d1bde88afca47 Mon Sep 17 00:00:00 2001 From: filifa Date: Sun, 20 Jul 2025 19:47:59 -0400 Subject: [PATCH] fix grammar --- notebooks/problem0066.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/notebooks/problem0066.ipynb b/notebooks/problem0066.ipynb index b3adc04..39f2b10 100644 --- a/notebooks/problem0066.ipynb +++ b/notebooks/problem0066.ipynb @@ -97,7 +97,7 @@ "$$x^2 - dy^2 = 1$$\n", "then $\\frac{x_0}{y_0}$ is a [convergent of the continued fraction](https://en.wikipedia.org/wiki/Simple_continued_fraction) of $\\sqrt{d}$. Specifically, if $p$ is the period of the continued fraction, then the first solution will be the $(p-1)$th convergent if $p$ is even, and the $(2p-1)$th convergent if $p$ is odd.\n", "\n", - "This is great for us, since there are algorithms to compute these convergents. We'll use SageMath here; see [problem 64](https://projecteuler.net/problem=64) for how to compute the partial denominators of the continued fraction of a square root, and see [problem 65](https://projecteuler.net/problem=65) for an algorithm that uses partial denominators to compute convergents of continued fractions (using SageMath's constructions adds overhead that makes this implementation a little slow, but it makes the code easier to read - and it's still considerably faster than using `solve_diophantine`)." + "This is great for us, since there are algorithms to compute these convergents. We'll use SageMath here; see [problem 64](https://projecteuler.net/problem=64) for how to compute the partial denominators of the continued fraction of a square root, and see [problem 65](https://projecteuler.net/problem=65) for an algorithm that uses partial denominators to compute convergents of continued fractions (SageMath's constructions make this implementation a little slow, but it makes the code easier to read - and it's still considerably faster than using `solve_diophantine`)." ] }, {