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A

angleofdarkness

$P=12(5^2+1)(5^4+1)(5^8+1)(5^{16}+1) $

\Rightarrow $2P=24(5^2+1)(5^4+1)(5^8+1)(5^{16}+1) \\ =(5^2-1)(5^2+1)(5^4+1)(5^8+1)(5^{16}+1) \\ =(5^4-1)(5^4+1)(5^8+1)(5^{16}+1) \\ =(5^8-1)(5^8+1)(5^{16}+1) \\ =(5^{16}-1)(5^{16}+1) \\ =5^{32}-1$

\Rightarrow $P=\dfrac{5^{32}-1}{2}$
 
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