Minimal entropy for endomorphisms of the circle

Let $f$ be an endomorphism (continuous map) of the circle which has two periodic points of period $m$ and $n$ respectively such that $m \geqslant 2,n \geqslant 2$ and $(m,n) = 1$, then topological entropy $h(f) \geqslant \log {\mu _{m,n}}$ where ${\mu _{m,n}}$ is the largest zero of the polynomial ${x^{m + n}} - {x^m} - {x^n} - 1$.