Show that if n is a positive integer, then fo(n) (26(n) $(2n) = if n is odd if n is even.
Show that if n is a positive integer, then fo(n) (26(n) $(2n) = if n is odd if n is even.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Problem 4:**
Show that if \( n \) is a positive integer, then:
\[
\phi(2n) =
\begin{cases}
\phi(n) & \text{if } n \text{ is odd} \\
2\phi(n) & \text{if } n \text{ is even}
\end{cases}
\]
Here, \(\phi(n)\) represents Euler's totient function, which counts the number of positive integers up to \( n \) that are relatively prime to \( n \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe87a569b-7721-4104-9b29-fedcf0a2817b%2Fbcf20054-d76d-40ec-addd-16217a6b3406%2Fax1lzlc_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 4:**
Show that if \( n \) is a positive integer, then:
\[
\phi(2n) =
\begin{cases}
\phi(n) & \text{if } n \text{ is odd} \\
2\phi(n) & \text{if } n \text{ is even}
\end{cases}
\]
Here, \(\phi(n)\) represents Euler's totient function, which counts the number of positive integers up to \( n \) that are relatively prime to \( n \).
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Given- n is a positive integer.
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