Question

CMR 2013^2013+2017^2017 chia hết cho 10

Answer 1

Ta có

\(2017^{2017}=\left(2017^{2016}\right).2017=\left(...1\right).2017=\left(...7\right)\)
\(2013^{2013}=\left(2013^{2012}\right).2013=\left(...1\right).2013=\left(...3\right)\)
\(\Rightarrow2013^{2013}+2017^{2017}=\left(...3\right)+\left(...7\right)=\left(...0\right)⋮10\)

Answer 2

\(2013^{2013}+2017^{2017}\)

Ta có:

\(2013^{2013}=\left(2013^{2012}\right).2013=\overline{...1}.2013=\overline{...3}\)

\(2017^{2017}=\left(2017^{2016}\right).2017=\overline{...1}.2017=\overline{...3}\)

\(\Rightarrow2013^{2013}+2017^{2017}=\overline{...3}+\overline{...7}=\overline{...0}⋮10\)

\(\Rightarrow2013^{2013}+2017^{2017}⋮10\)