Question

the number that exactly divides 3^41+3^42+3^43+3^44​

Answer 1

$\textbf{Given:}$

$\mathsf{3^{41}+3^{42}+3^{43}+3^{44}}$

$\textbf{To find:}$

$\textsf{The number that exactly divides}\;\mathsf{3^{41}+3^{42}+3^{43}+3^{44}}$

$\textbf{Solution:}$

$\textsf{Consider,}$

$\mathsf{3^{41}+3^{42}+3^{43}+3^{44}}$

$\mathsf{Taking\;3^{41}\;as\;common}$

$\mathsf{=3^{41}(1+3^1+3^2+3^3)}$

$\mathsf{=3^{41}(1+3+9+27)}$

$\mathsf{=3^{41}{\times}40}$

$\textsf{which is a multiple of 40}$

$\therefore\mathsf{40\;divides\;3^{41}+3^{42}+3^{43}+3^{44}\;exactly}$

$\textbf{Find more:}$

Find the remainder when 7^21+7^22+7^23+7^24 is divided by 25

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