Question

chứng minh rằng: 5^2022+2^2023 chia hết cho 3

Answer 1

Tham khảo

\(\text{+)}\)Ta có:\(5\equiv-1\left(mod3\right)\)

\(\Rightarrow5^{2022}\equiv\left(-1\right)^{2022}\left(mod3\right)\left(1\right)\)

\(\text{+)}\)Ta có:\(2\equiv-1\left(mod3\right)\)

\(\Rightarrow2^{2023}\equiv\left(-1\right)^{2023}\left(mod3\right)\left(2\right)\)

Từ \(\left(1\right)\) và \(\left(2\right)\Rightarrow5^{2022}+5^{2023}\equiv0\left(mod3\right)\)

Vậy...