Ta có:
\(M=36^{38}+41^{33}=\left(36^{38}-1\right)+\left(41^{33}+1\right)\)
\(\Rightarrow\left\{\begin{matrix}36^{38}-1=\left(36-1\right)\left(36^{37}+36^{36}+...+1\right)\\41^{33}+1=\left(41+1\right)\left(41^{32}-41^{31}+...+1\right)\end{matrix}\right.\)
\(\Rightarrow\left\{\begin{matrix}35\left(36^{37}+36^{36}+...+1\right)=5.7.Q⋮7\\42\left(41^{32}-41^{31}+...+1\right)=6.7.Q⋮7\end{matrix}\right.\)\(\Leftrightarrow M⋮7\)
Vậy \(M=36^{38}+41^{33}⋮7\) (Đpcm)
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