Câu hỏi của Trần Hồ Hoài An

Question

2. Chứng minh

a) 8⁷ - 2¹⁸ chia hết 14

b) 10⁶ - 5⁷ chia hết 59

Nguyễn Huệ Lam · Accepted Answer

$8^7-2^{18}=\left(2^3\right)^7-2^{18}=2^{21}-2^{18}=2^{17}.\left(2^4-2\right)=2^{17}.14⋮14.$

$10^6-5^7=\left(2.5\right)^6-5^7=2^6.5^6-5^7=5^6.\left(2^6-5\right)=5^5.59⋮59.$

Câu trả lời:

$8^7-2^{18}=\left(2^3\right)^7-2^{18}=2^{21}-2^{18}=2^{17}.\left(2^4-2\right)=2^{17}.14⋮14.$

$10^6-5^7=\left(2.5\right)^6-5^7=2^6.5^6-5^7=5^6.\left(2^6-5\right)=5^5.59⋮59.$

Kiệt Nguyễn · Answer

a) Ta có : $8^7-2^{18}=\left(2^3\right)^7-2^{17+1}$

$\Rightarrow8^7-2^{18}=2^{3\times7}-2^{17}\times2^1$

$\Rightarrow8^7-2^{18}=2^{21}-2^{17}\times2$

$\Rightarrow8^7-2^{18}=2^{17+4}-2^{17}\times2$

$\Rightarrow8^7-2^{18}=2^{17}\times2^4-2^{17}\times2$

$\Rightarrow8^7-2^{18}=2^{17}\left(2^4-2\right)$

$\Rightarrow8^7-2^{18}=2^{17}\left(16-2\right)$

$\Rightarrow8^7-2^{18}=2^{17}\times14$

$\Rightarrow\left(8^7-2^{18}\right)⋮14\left(\text{vì }14⋮14\right)$

b) Ta có : $10^6-5^7=\left(2\times5\right)^6-5^{6+1}$

$\Rightarrow10^6-5^7=2^6\times5^6-5^6\times5^1$

$\Rightarrow10^6-5^7=5^6\left(2^6-5^1\right)$

$\Rightarrow10^6-5^7=5^6\left(64-5\right)$

$\Rightarrow10^6-5^7=5^6\times59$

$\Rightarrow\left(10^6-5^7\right)⋮59\left(\text{vì }59⋮59\right)$