If \( (9+\sqrt{80})^{\mathrm{n}}=1+\mathrm{f} \) where \( \mathrm{I...

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If \( (9+\sqrt{80})^{\mathrm{n}}=1+\mathrm{f} \) where \( \mathrm{I}, \mathrm{n} \) are integers and \( 0\mathrm{f}1 \), then
\( \mathrm{P} \)
(A) \( \mathrm{I} \) is an odd integer for all \( \mathrm{n} \).
(B) I is an even integer for all \( n \).
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(C) \( (I+f)(1-f)=1 \)
(D) \( 1-\mathrm{f}=(9-\sqrt{80})^{\mathrm{n}} \)
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