Question

[Hoàng Thanh]

Cho ab=455^12. Tìm số dư khi chia a+b cho 4

Answer 1

[từ 1-9]

NX: \(455^{12}\equiv1\left(mod4\right)\)

\(\Rightarrow ab\equiv1\left(mod4\right)\)nên đặt \(a=4k+m,b=4h+n\left(k,h\in N:m,n\in[0,1,2,3]\right)\)

\(\Rightarrow mn\equiv1\left(mod4\right)\)

\(\Rightarrow\orbr{\begin{cases}m=n=1\\m=n=3\end{cases}}\)\(\Rightarrow m+n\equiv2\left(mod4\right)\)

Vậy ab chia 4 dư 2