From b7b7dbb6ec7bf609132ece889b24979fa3352193 Mon Sep 17 00:00:00 2001
From: sarthakgupta1907-cell <sarthakgupta1907@gmail.com>
Date: Mon, 2 Nov 2026 14:38:27 +0530
Subject: [PATCH] feat: add Euler totient function algorithm

---
 Maths/EulerTotient.js           | 29 ++++++++++++++++++++++++
 Maths/test/EulerTotient.test.js | 40 +++++++++++++++++++++++++++++++++
 2 files changed, 69 insertions(+)
 create mode 100644 Maths/EulerTotient.js
 create mode 100644 Maths/test/EulerTotient.test.js

diff --git a/Maths/EulerTotient.js b/Maths/EulerTotient.js
new file mode 100644
index 0000000000..af79f8cdfa
--- /dev/null
+++ b/Maths/EulerTotient.js
@@ -0,0 +1,29 @@
+/**
+ * @function eulerTotient
+ * @description Euler's totient function counts the positive integers up to n
+ *   that are relatively prime to n (i.e., gcd(k, n) = 1).
+ * @param {number} n - A positive integer greater than 0
+ * @returns {number} - Count of integers from 1 to n coprime to n
+ * @see https://en.wikipedia.org/wiki/Euler%27s_totient_function
+ * @example eulerTotient(9) => 6
+ * @example eulerTotient(1) => 1
+ */
+const eulerTotient = (n) => {
+  if (!Number.isInteger(n) || n < 1) {
+    throw new TypeError('Input must be a positive integer')
+  }
+  let result = n
+  let p = 2
+  let temp = n
+  while (p * p <= temp) {
+    if (temp % p === 0) {
+      while (temp % p === 0) temp = Math.floor(temp / p)
+      result -= Math.floor(result / p)
+    }
+    p++
+  }
+  if (temp > 1) result -= Math.floor(result / temp)
+  return result
+}
+
+export { eulerTotient }
diff --git a/Maths/test/EulerTotient.test.js b/Maths/test/EulerTotient.test.js
new file mode 100644
index 0000000000..f6527cbe17
--- /dev/null
+++ b/Maths/test/EulerTotient.test.js
@@ -0,0 +1,40 @@
+import { eulerTotient } from '../EulerTotient.js'
+
+describe('eulerTotient', () => {
+  test('eulerTotient(1) returns 1', () => {
+    expect(eulerTotient(1)).toBe(1)
+  })
+
+  test('eulerTotient(2) returns 1', () => {
+    expect(eulerTotient(2)).toBe(1)
+  })
+
+  test('eulerTotient(9) returns 6', () => {
+    expect(eulerTotient(9)).toBe(6)
+  })
+
+  test('eulerTotient(10) returns 4', () => {
+    expect(eulerTotient(10)).toBe(4)
+  })
+
+  test('eulerTotient(36) returns 12', () => {
+    expect(eulerTotient(36)).toBe(12)
+  })
+
+  test('eulerTotient of a prime returns prime minus 1', () => {
+    expect(eulerTotient(7)).toBe(6)
+    expect(eulerTotient(13)).toBe(12)
+  })
+
+  test('throws TypeError for zero', () => {
+    expect(() => eulerTotient(0)).toThrow(TypeError)
+  })
+
+  test('throws TypeError for negative input', () => {
+    expect(() => eulerTotient(-5)).toThrow(TypeError)
+  })
+
+  test('throws TypeError for float', () => {
+    expect(() => eulerTotient(1.5)).toThrow(TypeError)
+  })
+})