a/ Không chia hết cho 3 mới đung
\(\left\{{}\begin{matrix}6^{2n+1}⋮3\\5^{n+2}⋮̸3\end{matrix}\right.\) \(\Rightarrow6^{2n+1}+5^{n+2}⋮̸3\)
b/
\(2^{100}=2.2^{99}=2.\left(8\right)^{33}\)
Mà \(8\equiv-1\left(mod9\right)\Rightarrow8^{33}\equiv\left(-1\right)^{33}\left(mod9\right)\Rightarrow8^{33}\equiv\left(-1\right)\left(mod9\right)\)
\(\Rightarrow2.8^{33}\equiv-2\left(mod9\right)\Rightarrow2^{100}\) chia 9 dư \(9-2=7\)
\(2^{100}=\left(2^{10}\right)^{10}=1024^{10}\)
Mà \(1024\equiv-1\left(mod25\right)\Rightarrow1024^{10}\equiv\left(-1\right)^{10}\left(mod25\right)\Rightarrow1024^{10}\equiv1\left(mod25\right)\)
Vậy \(2^{100}\) chia 25 dư 1
