In this lesson, we explore the Möbius function, denoted as μ(n), a fundamental arithmetic function in number theory, often seen as a bridge between elementary number theory and advanced analytic concepts.

The Möbius function is deeply connected to the distribution of prime numbers through its crucial role in the Riemann Hypothesis. We will discuss how the Möbius function is related to this hypothesis through its connection to the Mertens function.

While the basic properties of the Möbius function are simple to understand, its connection to the Riemann Zeta Function is an advanced topic; to avoid making this lesson too heavy, we separated the Theorem you can find below, crucial to our demonstration, in an appendix.