MHB What Are the Real-Life Applications of the Euler Totient Function?

matqkks
Messages
280
Reaction score
5
What is most motivating and tangible way of introducing this function? Does it in itself have any real life applications that have an impact. I can only think of a^phi(n)=1 (mod n) which is powerful result but is this function used elsewhere.
 
Mathematics news on Phys.org
matqkks said:
What is most motivating and tangible way of introducing this function? Does it in itself have any real life applications that have an impact. I can only think of a^phi(n)=1 (mod n) which is powerful result but is this function used elsewhere.

One of the most remarkable application of the $\displaystyle \varphi(n)$ is the RSA Public Key Encryption...

RSA Encryption -- from Wolfram MathWorld

Kind regards

$\chi$ $\sigma$
 

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Thread 'Useless continued fraction for 1'

I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.
View full post »

Similar threads

How Is the Euler Totient Function Applied in Real Life?
Replies
3
Views
2K
MHB What is the role of Euler's Totient function in Fermat's Little Theorem?
Replies
6
Views
3K
I Can Angular Velocity Accurately Control Ragdoll Limbs in Game Physics?
Replies
6
Views
2K
MHB Why Does Only n=4 Satisfy the Equation g(n)=n-2 in Euler's Totient Function?
Replies
5
Views
2K
MHB Elaborations about Euler's Totient Function
Replies
8
Views
3K
ArXiv:1301.7652 and Euler homogeneous function theorem
Replies
6
Views
2K
Continued Fractions: Motivation & Real Life Applications
Replies
2
Views
2K
MHB Real Life Applications of Ceiling and Floor Functions
Replies
2
Views
5K
I Alternating Harmonic Numbers are cool, spread the word!
Replies
4
Views
2K
I What are the resources for Pythagorean triples?
Replies
10
Views
2K

Hot Threads

Recent Insights

Back
Top