\(2^{2n+1}+3^{2n+1}\text{ }\)
\(=4^n\times2+9^n\times3\)
\(=4^n\times2-9^n\times2+9^n\times5\)
\(=-2\left(9^n-4^n\right)+9^n\times5\)
\(9^n-4^n⋮9-4=5\Rightarrow-2\left(9^n-4^n\right)⋮5\)\(9^n\times5⋮5\)Vậy \(2^{2n+1}+3^{2n+1}⋮5\)
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