Chứng minh rằng: \(a)\ P={{7}^{19}}+{{7}^{20}}+{{7}^{21}}\) chia hết cho \(57\) \(b)\ Q={{32}^{567}}-{{32}^{566}}\) chia hết cho \(31\)
Chứng minh rằng: \(a)\ P={{7}^{19}}+{{7}^{20}}+{{7}^{21}}\) chia hết cho \(57\) \(b)\ Q={{32}^{567}}-{{32}^{566}}\) chia hết cho \(31\) Lời giải chi tiết: \(a)\ P={{7}^{19}}+{{7}^{20}}+{{7}^{21}} \\ ={{7}^{19}}+{{7}^{19}}.7+{{7}^{19}}{{.7}^{2}} \\ ={{7}^{19}}.\left( …