Question

Tìm số dư troh phép chia 3^100 cho 13.

Answer 1

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

\(\Rightarrow\left(3^3\right)^{33}\equiv1^{33}\left(mod13\right)\)

\(\Rightarrow3^{99}\equiv1\left(mod13\right)\Rightarrow3^{99}.3\equiv1.3\left(mod13\right)\Rightarrow3^{100}\equiv3\left(mod13\right)\)

Vậy 3^100 chia 13 dư 3

Answer 2

Tìm số dư cho phép chia 3¹⁰⁰ chia cho 13