If \( p \) is an odd prime and \( [x] \) denotes the greatest integ...

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If \( p \) is an odd prime and \( [x] \) denotes the greatest integer \( \leq x \), then
\[
\left[(2+\sqrt{3})^{p}\right]-2^{p+1}
\]
is divisible by
(a) 2
(b) \( p \)
(c) \( p-1 \)
(d) \( p+1 \)
\( \mathrm{P} \)
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