\(C=\left(4^{39}+4^{40}+4^{41}\right)\)
\(\Leftrightarrow C=4^{39}\left(1+4+4^2\right)\)
\(\Leftrightarrow C=4^{39}.21\)
\(\Leftrightarrow C=4^{38}.4.21\)
\(\Leftrightarrow C=4^{38}.84\)
\(\Leftrightarrow C=4^{38}.28.3\)
\(\Leftrightarrow C=28\left(4^{38}.3\right)\)
Vì có cơ số 3 nên C chia hết cho 3 (đpcm)
439+440+441
=439(1+4+42)
=439.21
=439.3.7
=438.3.4.7
=438.3.28 chia hết cho 28
Ta viết : \(C=4^{39}+4^{40}+4^{41}=4\left(4^{38}+4^{39}+4^{40}\right)\Rightarrow C⋮4\)
Lại viết : \(C=4^{39}\left(1+4+4^2\right)=4^{39}.21=4^{39}.3.7\)
\(\Rightarrow C⋮7\) mà (4;7) = 1
\(\Rightarrow C⋮28\)
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