From 7be8986c118686144d1d633a768017463f984b91 Mon Sep 17 00:00:00 2001
From: Mann Mehta <44433995+mann2108@users.noreply.github.com>
Date: Sun, 29 Mar 2020 17:18:49 +0530
Subject: [PATCH] Added eulers totient function in math

---
 math/eulers_totient_function.cpp | 48 ++++++++++++++++++++++++++++++++
 1 file changed, 48 insertions(+)
 create mode 100644 math/eulers_totient_function.cpp

diff --git a/math/eulers_totient_function.cpp b/math/eulers_totient_function.cpp
new file mode 100644
index 000000000..1d1d75edf
--- /dev/null
+++ b/math/eulers_totient_function.cpp
@@ -0,0 +1,48 @@
+#include<bits/stdc++.h>
+
+using namespace std;
+typedef long long int ll;
+
+/**
+
+Euler Totient Function also know as phi function.
+
+phi(n) = phi(p1^a1).phi(p2^a2)...
+where p1, p2,... are prime factor of n.
+
+3 Euler's Property:
+1. phi(prime_no) = prime_no-1
+2. phi(prime_no^k) = (prime_no^k - prime_no^(k-1))
+3. phi(a,b) = phi(a). phi(b) where a and b are relative primes.
+
+Applying this 3 property on the first equation.
+phi(n) = n. (1-1/p1). (1-1/p2). ...
+where p1,p2... are prime factors.
+
+Hence Implementation in O(sqrt(n)).
+
+*/
+
+ll phiFunction(ll n){
+    ll res = n;
+    for(ll i=2;i*i<=n;i++){
+        if(n%i==0){
+            while(n%i==0){
+                n/=i;
+            }
+            res-=res/i;
+        }
+    }
+    if(n>1)res-=res/n;
+    return res;
+}
+
+int main(){
+    ll t;
+    cin>>t;
+    while(t--){
+        ll n;
+        cin>>n;
+        cout<<phiFunction(n)<<endl;
+    }
+}