RSA encryption proof step explanation

[Leo Liu]

From the paper https://people.csail.mit.edu/rivest/Rsapaper.pdf
Can someone explain the green highlight to me please? Sorry that I can't type much because this is the final week. Thanks.

 

[Gaussian97]

It should be evident from equation 5

 

[fresh_42]

From $(5)$ we have
\begin{align*}
ed\equiv 1 \mod \phi(n) &\Longleftrightarrow \phi(n)\,|\,(ed-1) \\
&\Longleftrightarrow \phi(n)\cdot k = ed-1 \text{ for some } k \in \mathbb{Z}\\
&\Longleftrightarrow \phi(n)\cdot k +1 = ed \text{ for some } k \in \mathbb{Z}\\
&\Longrightarrow M^{\phi(n)\cdot k +1} =M^{ed}
\end{align*}