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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Vedclass · Accepted Answer

an odd prime integer

Vedclass · Answer

(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

Similar Questions

The remainder when $3^{37}$ is divided by $80$ is:

For all integers $n \geq 1$,which of the following is divisible by $9$?

For what values of $m \in \mathbb{N}$,does the divisibility $(x+y) \mid (x^m+y^m)$ hold?

If $(2021)^{3762}$ is divided by $17$,then the remainder is ........

If $n \in N$,then ${x^{2n - 1}} + {y^{2n - 1}}$ is divisible by

Vedclass Test Series

Exam Paper Generator

Online Exam Module