Question

[nguyễn minh quang]

CMR : ( 3^100 - 3 ) chia hết cho 13

Làm nhanh hộ mình rồi mìn tích cho

Answer 1

[pham trung thanh]

\(3^3\equiv1\left(mod13\right)\)

\(\Rightarrow3^{99}\equiv1\left(mod13\right)\)

\(\Rightarrow3^{100}\equiv3\left(mod13\right)\)

\(\Rightarrow3^{100}-3\equiv0\left(mod13\right)\)

\(\Rightarrow3^{100}-3⋮13\)