\(\phi\)nd the Remainder

\(\phi(n)\) is the number of positive integers less than \(n\) that are relatively prime to \(n.\)

Find the remainder when \(\phi\big(2^{2018} + 1\big)\) is divided by 4036.


Bonus: Generalize for the remainder when \(\phi(2^n+1)\) is divided by \(2n.\)

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