In order for us to apply Fermat's Little Theorem, we need \( p \neq 2\).

Breadcrumb 7: If \( p = 2 \), then \( 2 \mid f(2^n) \). We need another approach here.

**Exercise 10:** Deal with this yourself.

Now that I've walked you through how to figure out this proof from the end result, write out the proof as you would present it.

**Exercise 11:** Write out a complete proof to the original question.

Ponder this, and you are done.

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