If 2^{4n+3} + 3^{3n+1} is divisible by P for | vedclass

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(C) Let $f(n) = 2^{4n+3} + 3^{3n+1}$.For $n = 1$, $f(1) = 2^{4(1)+3} + 3^{3(1)+1} = 2^7 + 3^4 = 128 + 81 = 209$.For $n = 2$, $f(2) = 2^{4(2)+3} + 3^{3

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an odd prime integer

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(C) Let $f(n) = 2^{4n+3} + 3^{3n+1}$.For $n = 1$, $f(1) = 2^{4(1)+3} + 3^{3(1)+1} = 2^7 + 3^4 = 128 + 81 = 209$.For $n = 2$, $f(2) = 2^{4(2)+3} + 3^{3(2)+1} = 2^{11} + 3^7 = 2048 + 2187 = 4235$.We find the greatest common divisor of $209$ and $4235$.$209 = 11 	imes 19$.$4235 = 5 	imes 847 = 5 	imes 7 	imes 121 = 5 	imes 7 	imes 11^2$.The common divisor is $11$.Since $11$ is an odd prime number, $P = 11$ satisfies the condition.

If $2^{4n+3} + 3^{3n+1}$ is divisible by $P$ for all natural numbers $n$, then $P$ is

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