MHB How Can I Solve a Problem Using Euler's Totient Function for Odd Prime Numbers?

  • Thread starter Thread starter goody1
  • Start date Start date
  • Tags Tags
    Function
AI Thread Summary
To solve problems using Euler's Totient Function for odd prime numbers, it's essential to understand its definition and application. The discussion begins by examining specific examples, such as $\varphi(5)$, $\varphi(7)$, and $\varphi(11)$, to identify a general rule. For any odd prime number \( n \), the value of \( \varphi(n) \) represents the count of integers less than \( n \) that are coprime to \( n \). This foundational understanding is crucial for tackling more complex problems involving odd primes. Engaging with these examples helps clarify the function's properties and its implications.
goody1
Messages
16
Reaction score
0
Hello everyone, can anybody help me with this problem?

pic.png


The solution is for all odd prime numbers, but I have no idea how to solve it.
Any help will be greatly appreciated.
 
Physics news on Phys.org
Hi goody,

Let's take this one step at a time by first looking at the right hand side, then the left hand side for odd primes. We will worry about the non-odd prime case later.

Let's think of some examples first. What is the value of $\varphi(5)$? How about $\varphi(7)$ and $\varphi(11)$? Can you see a general rule emerging from these examples? Now, if $n$ is an odd prime, what should the value of $\varphi(n)$ be? In other words, how many numbers less than $n$ do not share a common divisor with $n$?
 

Thread 'Deductive proof in logic formal systems'

I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...
View full post »

Similar threads

I What is the probability that the product of the digits is odd?
Replies
13
Views
2K
B Are All Imaginable Integer Series Necessarily Infinite?
Replies
17
Views
2K
A Is it required to use the Reimann function to solve the problem?
Replies
8
Views
1K
MHB A Subset of a Graph with No Perfect Matching
Replies
1
Views
2K
A Number of unequal integers with sum S
Replies
12
Views
2K
Can 4 distinct prime numbers be related in such a way?
Replies
14
Views
3K
I Number of Integers (<N) divisible only by one power of 2
Replies
6
Views
1K
I Difference between relative risk and odds ratio
Replies
7
Views
3K
Exercise on (ir)rational numbers
Replies
1
Views
1K
MHB Next set of prime birthdays for three brothers
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top