Added EulersTotientFunction function to the Maths Folder

Author: sandyboypraper

Maths/EulersTotientFunction.js

@@ -0,0 +1,28 @@
+/*
+    author sandyboypraper
+
+    Here is the EulerTotientFunction.
+    it is also represented by phi
+
+    so EulersTotientFunction(n) (or phi(n)) is the count of numbers in {1,2,3,....,n} that are relatively
+    prime to n, i.e., the numbers whose GCD (Greatest Common Divisor) with n is 1.
+*/
+
+const gcd_two_numbers = (x, y) => {
+    // x is smaller than y
+    // let gcd of x and y is gcdXY
+    // so it devides x and y completely
+    // so gcdXY should also devides y%x (y = gcdXY*a and x = gcdXY*b and y%x = y - x*k so y%x = gcdXY(a - b*k))
+    // and gcd(x,y) is equals to gcd(y%x , x)
+    return x == 0 ? y : gcd_two_numbers(y%x , x);
+}
+
+const EulersTotientFunction = (n) => {
+    let countOfRelativelyPrimeNumbers = 1;
+    for(let iterator = 2; iterator<=n; iterator++)
+        if(gcd_two_numbers(iterator , n) == 1)countOfRelativelyPrimeNumbers++;
+    
+    return countOfRelativelyPrimeNumbers;
+}
+
+export {EulersTotientFunction}

Maths/test/EulersTotientFunction.test.js

@@ -0,0 +1,11 @@
+import { EulersTotientFunction } from '../EulersTotientFunction';
+
+describe('eulersTotientFunction', () => {
+  it('is a function', () => {
+    expect(typeof EulersTotientFunction).toEqual('function')
+  })
+  it('should return the phi of a given number', () => {
+    const phiOfNumber = EulersTotientFunction(10)
+    expect(phiOfNumber).toBe(4)
+  })
+})

package-lock.json

@@ -27,4 +27,4 @@
     "jest": "^26.4.2",
     "standard": "^14.3.4"
   }
-}
+}