Question

chứng minh rằng : \(\left(8^8+2^{20}\right)\)chia hết cho 17

Answer 1

\(=\left(2^3\right)^8+2^{20}\)

\(=2^{24}+2^{20}\)

\(=2^{20}.\left(2^4+1\right)\)\(=2^{20}.17⋮17\)

Vậy ...

Answer 2

8⁸ + 2²⁰ 

= (2³)⁸ + 2²⁰

= 2²⁴ + 2²⁰

= 2²⁰.2⁴ + 2²⁰.1

= 2²⁰(2⁴ + 1)

= 2²⁰.17 ⋮ 17 (đpcm)

Answer 3

(8^8+2^20)

=(2^3)^8+2^20

=2^24+2^20

=2^44

chúc bạn học giỏi

Answer 4

\(8^8+2^{20}\)

\(=\left(2^3\right)^8+2^{20}\)

\(=2^{24}+2^{20}\)

\(=2^{20}.\left(2^4+1\right)\)

\(=2^{20}.\left(16+1\right)\)

\(=2^{20}.17\)

Ta  có: \(\hept{\begin{cases}17⋮17\\2^{20}\inℕ\end{cases}\Rightarrow}17.2^{20}⋮17\)

\(\Rightarrow8^8+2^{20}⋮17\)

                 đpcm

Tham khảo nhé~

Answer 5

A=2^2+8^20 chia hết cho 17