Câu 1:
Ta có:
\(2^6\equiv-1\left(mod13\right)\Rightarrow2^{70}\equiv2^4.-1\left(mod13\right)\)
\(3^3\equiv1\left(mod13\right)\Rightarrow3^{70}\equiv3\left(mod13\right)\)
\(\Rightarrow2^{70}+3^{70}\equiv13\left(mod13\right)\equiv0\left(mod13\right)⋮13\left(dpcm\right)\)
câu 2: tìm số dư khi chia
a, 5^1000 cho 6
b, 4^2018 cho 3;15;13
c, 1997^2019 cho 9
\(Taco:\)
\(5\equiv-1\left(mod6\right)\Rightarrow5^{1000}\equiv\left(-1\right)^{1000}\left(mod6\right)\)
\(\Rightarrow5^{1000}\equiv1\left(mod6\right)\)
Vậy 5^1000 chia 6 dư 1
