Question

Chứng minh:

a)(8¹⁰ - 8⁹ - 8⁸) \(⋮\)55

b)(10⁹ + 10⁸ + 10⁷)\(⋮\)111

Answer 1

a) Ta có: 

\(8^{10}-8^9-8^8=8^8.\left(8^2-8-1\right)=8^8.55⋮55\)

\(\Rightarrow8^{10}-8^9-8^8⋮55\)

b) Ta có:

\(10^9+10^8+10^7=10^7.\left(10^2+10+1\right)=10^7.111⋮111\)

\(\Rightarrow10^9+10^8+10^7⋮111\)

Answer 2

\(8^{10}-8^9-8^8=8^8\left(8^2-8-1\right)=8^8\times55⋮55\)

\(10^9+10^8+10^7=10^7\left(10^2+10+1\right)=10^7\times111⋮111\)