From 0ce65b7a398607a570fbaf4251663c098d238b8d Mon Sep 17 00:00:00 2001 From: filifa Date: Sun, 20 Jul 2025 18:00:23 -0400 Subject: [PATCH] change wording --- notebooks/problem0048.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/notebooks/problem0048.ipynb b/notebooks/problem0048.ipynb index 68a5f96..6e2ed91 100644 --- a/notebooks/problem0048.ipynb +++ b/notebooks/problem0048.ipynb @@ -41,7 +41,7 @@ "$$a^{2x} = (a^x)^2$$\n", "$$a^{2x+1} = a(a^x)^2$$\n", "$$ab \\bmod{m} = (a \\bmod{m})(b \\bmod{m}) \\bmod{m}$$\n", - "The first two properties allows us to recursively break up a large power into two products (if the exponent is even) or three products (if the exponent is odd), a process known as [exponentiation by squaring](https://en.wikipedia.org/wiki/Exponentiation_by_squaring). The third property then allows us to distribute the modulus over multiplication. In tandem, these properties allow us to compute large powers with fewer multiplications, while also using less memory by keeping intermediate values small.\n", + "The first two properties allows us to recursively break up a large power into two multiplications (if the exponent is even) or three multiplications (if the exponent is odd), a process known as [exponentiation by squaring](https://en.wikipedia.org/wiki/Exponentiation_by_squaring). The third property then allows us to distribute the modulus over multiplication. In tandem, these properties allow us to compute large powers with fewer multiplications, while also using less memory by keeping intermediate values small.\n", "\n", "Interestingly, there is no known efficient algorithm for reversing this calculation, i.e. computing the [discrete logarithm](https://en.wikipedia.org/wiki/Discrete_logarithm).\n", "\n",