Question

Tìm số dư trong phép chia 109^345 cho 14

Answer 1

109^{345}=109^{3.115}=(109^{Q(14)})^{115}

Answer 2

\(109^3\equiv1\left(mod7\right)\)

\(\Rightarrow109^{\left(3k+r\right)}\equiv109^r\left(mod7\right)\)

Mà: 345 = 0 (mod 7)

\(\Rightarrow109^{345}=109^{\left(3.115+0\right)}\equiv109^0=1\left(mod7\right)\)

\(\Rightarrow109^{345}:7\)dư 1