2. Find all positive integers n such that 4 ( 12 ) has the value d) 6 e) 14 f) 24. b) c) 1 बल

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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**Problem 2: Finding Positive Integers with Specific Euler's Totient Function Values**

Consider the following problem:

Find all positive integers \( n \) such that the Euler's totient function \( \phi(n) \) has the following values:

a) 1  
b) 2  
c) 3  
d) 6  
e) 14  
f) 24

**Explanation:**

Euler's totient function \( \phi(n) \) is a number-theoretic function that counts the positive integers up to a given integer \( n \) that are relatively prime to \( n \). This problem asks you to find the integers \( n \) for which the totient function yields specific values.
Transcribed Image Text:**Problem 2: Finding Positive Integers with Specific Euler's Totient Function Values** Consider the following problem: Find all positive integers \( n \) such that the Euler's totient function \( \phi(n) \) has the following values: a) 1 b) 2 c) 3 d) 6 e) 14 f) 24 **Explanation:** Euler's totient function \( \phi(n) \) is a number-theoretic function that counts the positive integers up to a given integer \( n \) that are relatively prime to \( n \). This problem asks you to find the integers \( n \) for which the totient function yields specific values.
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