Question

chứng minh rằng : \(8^7-2^{18}\) chia hết cho 14

Answer 1

\(8^7-2^{18}\\ =\left(2^3\right)^7-2^{18}\\ =2^{21}-2^{18}\\ =2^{17}\cdot\left(2^4-2\right)\\ =2^{17}\cdot14⋮14\)

Vậy \(8^7-2^{18}⋮14\)

Answer 2

\(8^7-2^{18}\)

\(=\left(2^3\right)^7-2^{18}\)

\(=2^{21}-2^{18}\)

\(=2^{18}.2^3-2^{18}.1\)

\(=2^{18}.8-2^{18}.1\)

\(=2^{18}\left(8-1\right)\)

\(=2^{18}.7\)

\(=2^{17}.14⋮14\)

\(\rightarrowđpcm\)