From 7b5c628e89c834a3e8f018be0b1f3f146965bf0f Mon Sep 17 00:00:00 2001 From: Trashtalk Date: Fri, 31 May 2019 16:02:13 +0200 Subject: [PATCH 1/3] Added a proof for the Euclidean Algorithm --- contents/euclidean_algorithm/euclidean_algorithm.md | 6 ++++++ 1 file changed, 6 insertions(+) diff --git a/contents/euclidean_algorithm/euclidean_algorithm.md b/contents/euclidean_algorithm/euclidean_algorithm.md index 4ff49152f..26c308501 100644 --- a/contents/euclidean_algorithm/euclidean_algorithm.md +++ b/contents/euclidean_algorithm/euclidean_algorithm.md @@ -166,6 +166,12 @@ Here's a video on the Euclidean algorithm: +## Proof + +Some intuition as to why the Euclidean Algorithm works lies in it's proof. Only a proof for the subtraction method will be given at this point, but the modular version follows the same line of reasoning. + +Given two positive integers $$a$$ and $$b$$, they have a greatest common divisor $$d$$. There is always a common divisor, because every number is divisable by 1. Since $$a$$ and $$b$$ is divisable by $$d$$, $$a - b$$ is also divisable by $$d$$ ($$b < a$$). Let's call this value $$c$$. Now we once more have two numbers $$b$$ and $$c$$, which are both divisable by $$d$$. This process can be continued until the values are equal: this is the greatest common divisor $$d$$. + ## Example Code {% method %} From 131ae549231b39174f6379b0247af56efc827b9c Mon Sep 17 00:00:00 2001 From: Trashtalk Date: Fri, 31 May 2019 16:06:17 +0200 Subject: [PATCH 2/3] Revert "Added a proof for the Euclidean Algorithm" This reverts commit 7b5c628e89c834a3e8f018be0b1f3f146965bf0f. --- contents/euclidean_algorithm/euclidean_algorithm.md | 6 ------ 1 file changed, 6 deletions(-) diff --git a/contents/euclidean_algorithm/euclidean_algorithm.md b/contents/euclidean_algorithm/euclidean_algorithm.md index 26c308501..4ff49152f 100644 --- a/contents/euclidean_algorithm/euclidean_algorithm.md +++ b/contents/euclidean_algorithm/euclidean_algorithm.md @@ -166,12 +166,6 @@ Here's a video on the Euclidean algorithm: -## Proof - -Some intuition as to why the Euclidean Algorithm works lies in it's proof. Only a proof for the subtraction method will be given at this point, but the modular version follows the same line of reasoning. - -Given two positive integers $$a$$ and $$b$$, they have a greatest common divisor $$d$$. There is always a common divisor, because every number is divisable by 1. Since $$a$$ and $$b$$ is divisable by $$d$$, $$a - b$$ is also divisable by $$d$$ ($$b < a$$). Let's call this value $$c$$. Now we once more have two numbers $$b$$ and $$c$$, which are both divisable by $$d$$. This process can be continued until the values are equal: this is the greatest common divisor $$d$$. - ## Example Code {% method %} From 470f429243fd250476a29897acabfa23de1dd518 Mon Sep 17 00:00:00 2001 From: Trashtalk Date: Fri, 31 May 2019 16:12:05 +0200 Subject: [PATCH 3/3] Added a proof to the euclidean algorithm. --- contents/euclidean_algorithm/euclidean_algorithm.md | 6 ++++++ 1 file changed, 6 insertions(+) diff --git a/contents/euclidean_algorithm/euclidean_algorithm.md b/contents/euclidean_algorithm/euclidean_algorithm.md index 4ff49152f..26c308501 100644 --- a/contents/euclidean_algorithm/euclidean_algorithm.md +++ b/contents/euclidean_algorithm/euclidean_algorithm.md @@ -166,6 +166,12 @@ Here's a video on the Euclidean algorithm: +## Proof + +Some intuition as to why the Euclidean Algorithm works lies in it's proof. Only a proof for the subtraction method will be given at this point, but the modular version follows the same line of reasoning. + +Given two positive integers $$a$$ and $$b$$, they have a greatest common divisor $$d$$. There is always a common divisor, because every number is divisable by 1. Since $$a$$ and $$b$$ is divisable by $$d$$, $$a - b$$ is also divisable by $$d$$ ($$b < a$$). Let's call this value $$c$$. Now we once more have two numbers $$b$$ and $$c$$, which are both divisable by $$d$$. This process can be continued until the values are equal: this is the greatest common divisor $$d$$. + ## Example Code {% method %}