Question

[Linh Le]

chứng minh rằng: A = 22n+1+32n+1 chia hết cho 5

giúp nhóa. tick cho

Answer 1

[Phương An]

\(2^{2n+1}+3^{2n+1}\text{ }\)

\(=4^n\times2+9^n\times3\)

\(=4^n\times2-9^n\times2+9^n\times5\)

\(=-2\left(9^n-4^n\right)+9^n\times5\)

• \(9^n-4^n⋮9-4=5\Rightarrow-2\left(9^n-4^n\right)⋮5\)
• \(9^n\times5⋮5\)

Vậy \(2^{2n+1}+3^{2n+1}⋮5\)

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