ta có : \(3^2\equiv2\left(mod7\right)\) \(\Rightarrow3^6=\left(3^2\right)^3\equiv1\left(mod7\right)\)
\(\Rightarrow\left(3^6\right)\equiv1\left(mod7\right)\)hay \(3^{1998}\equiv1\left(mod7\right)\)
mặt khác : \(3^2\equiv2\left(mod7\right)\)nên \(3^{2000}=3^{1998}.3^2\equiv1.2\left(mod7\right)\)
hay \(3^{2000}\div7\) dư \(2\)