Number Theory Euler Totient or Phi Function

[matqkks]

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.

 

[chisigma]

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

$\chi$ $\sigma$