# One of three of a kind - Part (3) - Final

**Number Theory**Level 3

\[\Large \prod_{n=1}^{\infty} \left(1-\frac{1}{\phi^n}\right)^{[\mu(n)-\varphi(n)]/n}\]

What is the value of the product above?

Note: \(\varphi\) is the Euler totient function, \(\mu\) is the Moebius function, and \(\phi = \dfrac{1+\sqrt5}{2}\) is the golden ratio.