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

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The Euler Totient Function, φ(n), is notably applied in RSA Public Key Encryption, which secures digital communications. Its significance lies in the property that a^φ(n) ≡ 1 (mod n), which is crucial for encryption and decryption processes. The discussion highlights the need for tangible methods to introduce the function, emphasizing its practical implications in cryptography. Overall, the Euler Totient Function plays a vital role in modern security systems, showcasing its real-life applications. Understanding its applications can enhance appreciation for its mathematical importance.
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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.
 
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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 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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