Add Euler's Totient Function

Add Euler's Totient Function in math directory

math/eulers_totient_function.cpp

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+/// C++ Program to find Euler Totient Function
+#include<iostream>
+
+/*
+ * Euler Totient Function is also known as phi function.
+ * phi(n) = phi(p1^a1).phi(p2^a2)...
+ * where p1, p2,... are prime factors of n.
+ * 3 Euler's properties:
+ * 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 properties 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)).
+ * phi(100) = 40
+ * phi(1) = 1
+ * phi(17501) = 15120
+ * phi(1420) = 560
+ */
+
+// Function to caculate Euler's totient phi
+int phiFunction(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() {
+    int n;
+    std::cin >> n;
+    std::cout << phiFunction(n);
+}