Deck of 52 Cards returns to Original Order after 52 Modified Perfect Faro Shuffles/Proof 2

Proof
From Number of Modified Perfect Faro Shuffles to return Deck of Cards to Original Order, the cards of $D$ will return to their original order after $n$ such shuffles, where:
 * $2^n \equiv 1 \pmod {53}$

By Fermat's Little Theorem:
 * $2^{52} \equiv 1 \pmod {53}$

So the cards of $D$ will return to their original order after $52$ modified perfect faro shuffles.