Question

Chứng tỏ: \(8^7-2^{18}⋮14\)

Answer 1

* Trả lời:

\(8^7-2^{18}⋮14\)

\(\Leftrightarrow\left(2^3\right)^7-2^{18}⋮14\)

\(\Leftrightarrow2^{21}-2^{18}⋮14\)

\(\Leftrightarrow2^{18}.\left(2^3-1\right)⋮14\)

\(\Leftrightarrow2^{18}.7⋮14\)

\(\Leftrightarrow2^{17}.2.7⋮14\)

\(\Leftrightarrow2^{17}.14⋮14\)

\(\Rightarrow8^7-2^{18}⋮14\)

Answer 2

8⁷-2¹⁸ =(2³)⁷-2¹⁸ =2²¹-2¹⁸=2¹⁸*(2³-1) =2¹⁸*7 =2¹⁷*2*7 =2¹⁷*14 chia hết cho 14

=> 8⁷-2¹⁸ chia hết cho 14 (đpcm)