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Prove by mathematical induction that $4$ is a factor of $9^n - 5^n\,\forall n\geq1$.

Please have a look at my attempt if it is correct or not. enter image description here

an4s
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uniBoi
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1 Answers1

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Everything is ok, except the last line where you used $ 4(9k+5^n) = 4n.$

As you notice, n is used to mean two different things.

Change the last $4n$ to $4m$ and you have a good proof.

Mohammad Riazi-Kermani
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