Added Some number theory ques in cpp

binary exponent loop.cpp

@@ -0,0 +1,28 @@
+#include <bits/stdc++.h>
+using namespace std;
+long long binpow(long long a, long long b)
+{
+	long long res = 1;
+	while (b > 0) {
+		if (b & 1)
+			res = res * a;
+		a = a * a;
+		b >>= 1;
+	}
+	return res;
+}
+
+int main()
+{
+	ios_base::sync_with_stdio(false);
+	cin.tie(NULL);
+	cout.tie(NULL
+	         long int base, power = 1, inputpower;
+	         cin >> base >> inputpower;
+	         long long int ans = 1;
+
+
+
+	         return 0;
+}
+

binary exponent recursive.cpp

@@ -0,0 +1,29 @@
+#include <bits/stdc++.h>
+using namespace std;
+long int bin_exp(long int base , long int power )
+{
+    if(power==0)
+    {
+        return 1;
+    }
+    else
+    {
+        long int temp =bin_exp(base,power/2);
+        if(power%2 == 0)
+            return (temp*temp);
+        else
+            return ((temp*temp)*base);
+    }
+}
+
+int main()
+{
+    ios_base::sync_with_stdio(false);
+    cin.tie(NULL);
+    cout.tie(NULL);
+    long int power,base;
+    cin>>base>>power;
+    cout<<bin_exp(base,power);
+
+    return 0;
+}

et or pfi using seive way.cpp

@@ -0,0 +1,40 @@
+#include <bits/stdc++.h>
+using namespace std;
+int phi(int n) {
+    int result = n;
+    for (int i = 2; i * i <= n; i++) {
+        if (n % i == 0) {
+            while (n % i == 0)
+                n /= i;
+            result -= result / i;
+        }
+    }
+    if (n > 1)
+        result -= result / n;
+    return result;
+}
+int main()
+{
+    ios_base::sync_with_stdio(false);
+    cin.tie(NULL);
+    cout.tie(NULL);
+    const long int MAX = 100;
+    int etf[MAX + 1];
+    for(int i=0;i<=MAX;i++)
+        etf[i] = i;
+    for(int i=2;i*i<=MAX;i++)
+    {
+        if(etf[i]== i)
+        {
+            for(long int j = i; j<=MAX ; j+=i)
+            {
+                etf[j] -= etf[j]/i;
+            }
+        }
+
+    }
+    for(int i=1;i<=25;i++)
+        cout<<"  "<<i<<"  "<<etf[i]<<"  ";
+
+    return 0;
+}

etf or phi in sqrt(n).cpp

@@ -0,0 +1,29 @@
+#include <bits/stdc++.h>
+using namespace std;
+int phi(int n)
+{
+    int result = n;
+    for (int i = 2; i * i <= n; i++)
+    {
+        if (n % i == 0)
+        {
+            while (n % i == 0)
+                n /= i;
+            result -= result / i;
+        }
+    }
+    if (n > 1)
+        result -= result / n;
+    return result;
+}
+
+int main()
+{
+    ios_base::sync_with_stdio(false);
+    cin.tie(NULL);
+    cout.tie(NULL);
+    int n;
+    cin>>n;
+    cout<<phi(n);
+    return 0;
+}

euclid extended.cpp

@@ -0,0 +1,91 @@
+#include <bits/stdc++.h>
+using namespace std;
+#define IOS ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
+#define endl "\n"
+#define int long long
+long long MOD = 1e9 + 7;
+
+long long gcdsimple(long long a,long long b){
+    if(b==0)
+        return a;
+    else
+        return gcd(b,a%b);
+}
+long long mod_pow(long long x, long long y, long long p)
+{
+    long long res = 1;
+
+    x = x % p;
+
+    if (x == 0) return 0;
+
+    while (y > 0)
+    {
+
+        if (y & 1)
+            res = (res * x) % p;
+
+
+        y = y >> 1;
+        x = (x * x) % p;
+    }
+    return res;
+}
+
+long long bin_pow(long long a, long long b)
+{
+    long long res = 1;
+    while (b > 0) {
+        if (b & 1)
+            res = res * a;
+        a = a * a;
+        b >>= 1;
+    }
+    return res;
+}
+long long multi(long long a , long long b , long long m)
+{
+    long long res = 0;
+    a = a%m;
+    while (b > 0) {
+        if (b & 1)
+            res = (res + a)%m;
+        a = (a%m + a%m)%m;
+        b >>= 1;
+    }
+    return res;
+
+}
+int gcdextended(int a, int b, int& x, int& y)
+{
+    if (b == 0) {
+        x = 1;
+        y = 0;
+        return a;
+    }
+    int x1, y1;
+    int d = gcd(b, a % b, x1, y1);
+    x = y1;
+    y = x1 - y1 * (a / b);
+    return d;
+}
+int gcd(int a, int b, int& x, int& y)
+{
+    x = 1, y = 0;
+    int x1 = 0, y1 = 1, a1 = a, b1 = b;
+    while (b1) {
+        int q = a1 / b1;
+        tie(x, x1) = make_tuple(x1, x - q * x1);
+        tie(y, y1) = make_tuple(y1, y - q * y1);
+        tie(a1, b1) = make_tuple(b1, a1 - q * b1);
+    }
+    return a1;
+}
+int32_t main()
+{
+    IOS;
+
+
+
+    return 0;
+}

euclidproblem.cpp

@@ -0,0 +1,36 @@
+#include <bits/stdc++.h>
+using namespace std;
+#define IOS ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
+#define endl "\n"
+#define int long long
+long long MOD = 1e9 + 7;
+
+long long gcd(long long a , long long b , long long& x , long long& y)
+{
+    if(b==0)
+    {
+        x = 1;
+        y = 0;
+        return a;
+    }
+    long long x1,y1;
+    long long d = gcd(b,a%b,x1,y1);
+    x = y1;
+    y = x1 - y1 * (a / b);
+    return d;
+}
+int32_t main()
+{
+    IOS;
+    int a,b,x,y,ans;
+    while(scanf("%lld %lld", &a, &b) == 2)
+    {
+        ans = gcd(a,b,x,y);
+        cout<<x<<" "<<y<<" "<<ans<<"\n";
+    }
+
+
+
+
+    return 0;
+}

gcd.cpp

@@ -0,0 +1,26 @@
+#include <bits/stdc++.h>
+using namespace std;
+int gcd(int a,int b)
+{
+    if(b==0)
+    {
+        return a;
+    }
+    else
+    {
+        return gcd(b,a%b);
+    }
+}
+
+int main()
+{
+    ios_base::sync_with_stdio(false);
+    cin.tie(NULL);
+    cout.tie(NULL);
+    cout<<gcd(12,18);
+
+
+
+    return 0;
+}
+

modular exponent loop.cpp

@@ -0,0 +1,32 @@
+#include <iostream>
+using namespace std;
+int power(int x, unsigned int y, int p)
+{
+	int res = 1;
+
+	x = x % p;
+
+	if (x == 0) return 0;
+
+	while (y > 0)
+	{
+
+		if (y & 1)
+			res = (res * x) % p;
+
+
+		y = y >> 1;
+		x = (x * x) % p;
+	}
+	return res;
+}
+
+int main()
+{
+	int x = 2;
+	int y = 5;
+	int p = 13;
+	cout << "Power is " << power(x, y, p);
+	return 0;
+}
+

modular exponent recursion.cpp

@@ -0,0 +1,30 @@
+#include <bits/stdc++.h>
+using namespace std;
+long int bin_exp(long int base , long int power, int m )
+{
+    base = base % m;
+    if (power == 0)
+    {
+        return 1;
+    }
+    else
+    {
+        long int temp = bin_exp(base, power / 2);
+        if (power % 2 == 0)
+            return ((temp % m) * (temp % m)) % m;
+        else
+            return ((temp % m) * (temp % m) * base) % m;
+    }
+}
+
+int main()
+{
+    ios_base::sync_with_stdio(false);
+    cin.tie(NULL);
+    cout.tie(NULL);
+    long int power, base;
+    cin >> base >> power;
+    cout << bin_exp(base, power);
+
+    return 0;
+}