fix grammar

This commit is contained in:
filifa 2025-07-20 19:47:59 -04:00
parent d6f896128d
commit 6fbee468b5
1 changed files with 1 additions and 1 deletions

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@ -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`)."
]
},
{