From ade147753ac584603780d7726796ff75afc8bcb3 Mon Sep 17 00:00:00 2001
From: "Paulo H. Lamounier" <53798700+Nanashii76@users.noreply.github.com>
Date: Tue, 4 Jun 2024 12:21:04 -0300
Subject: [PATCH] number theory problems

---
 part1/coprimeDivisor.cpp      | 24 +++++++++++++++++++
 part1/extendendEuclideans.cpp | 45 +++++++++++++++++++++++++++++++++++
 part1/gcd.cpp                 | 19 +++++++++++++++
 3 files changed, 88 insertions(+)
 create mode 100644 part1/coprimeDivisor.cpp
 create mode 100644 part1/extendendEuclideans.cpp
 create mode 100644 part1/gcd.cpp

diff --git a/part1/coprimeDivisor.cpp b/part1/coprimeDivisor.cpp
new file mode 100644
index 0000000..4d7921e
--- /dev/null
+++ b/part1/coprimeDivisor.cpp
@@ -0,0 +1,24 @@
+#include<bits/stdc++.h>
+using namespace std;
+
+int gcd(int a, int b) {return b==0?a:gcd(b,a%b);}
+
+int solve(int a, int b){
+    
+    int value = 1, x = 0;
+    while(value < max(a,b)) {
+        if(a%value == 0 and gcd(value,b)==1)
+            x = value;
+        value++;
+    }
+    
+    return x;
+}
+
+int main(){
+
+    int a,b; cin >> a >> b;
+    cout << solve(a,b) << endl;
+
+    return 0;
+}
\ No newline at end of file
diff --git a/part1/extendendEuclideans.cpp b/part1/extendendEuclideans.cpp
new file mode 100644
index 0000000..d1365da
--- /dev/null
+++ b/part1/extendendEuclideans.cpp
@@ -0,0 +1,45 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+/*
+    find the values of x and y thats
+
+    A * x + B * y = gcd(A,B)
+
+    where A and B are inputs
+
+*/
+int gcd(int a, int b) {
+    return b==0?a:gcd(b,a%b);
+}
+
+pair<int,int> extendedGCD(int a, int b) {
+
+    // base case
+    if(b==0) {
+        // returning the values of x and y
+        return {1,0};
+    }
+
+    pair<int,int> result = extendedGCD(b,a%b);
+    int smallX = result.first;
+    int smallY = result.second;
+
+    int x = smallY;
+    int y = smallX - floor(a/b)*smallY;
+
+    return {x,y};
+
+}
+
+
+int main(){
+
+    int a,b; cin >> a >> b;
+    // a x + b y = gcd(a,b);
+    pair<int,int> ans = extendedGCD(a,b);
+    cout << ans.first << " " << ans.second << endl;
+
+    return 0;
+}
+
diff --git a/part1/gcd.cpp b/part1/gcd.cpp
new file mode 100644
index 0000000..e230e4d
--- /dev/null
+++ b/part1/gcd.cpp
@@ -0,0 +1,19 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+int gcd(int a, int b) {
+
+    if(b == 0)
+        return a;
+    
+    return gcd(b,a%b);
+
+}
+
+int main(){
+
+    int a,b; cin >> a >> b;
+    cout << gcd(a,b) << endl;
+
+    return 0;
+}
\ No newline at end of file