Euler's Totient Function: Phi, Primes, and the Geometry of Security

We dive into Euler’s totient function, phi(n), counting how many integers less than n are coprime to n. From Euler’s product formula to Gauss’s polygon trick (phi(n) as a power of 2), we’ll explore the surprising links between primes, circles, and geometry. We’ll also connect totients to the distribution of primes and pi, and show how RSA cryptography relies on these ideas to secure digital communication. A ride through number theory’s hidden crossroads, with intuition and concrete examples.

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