Question

[Trần Hồ Hoài An]

2. Chứng minh 

a) 8⁷  - 2¹⁸ chia hết 14

b) 10⁶ - 5⁷ chia hết 59

Answer 1

[Nguyễn Huệ Lam]

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

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

Answer 2

[Kiệt Nguyễn]

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

\(\Rightarrow10^6-5^7=2^6\times5^6-5^6\times5^1\)

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

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

\(\Rightarrow10^6-5^7=5^6\times59\)

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