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PROVE THIS.... THIS IS A BIT HARDER

Note by Sayan Chaudhuri
4 years, 7 months ago

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Hint : Induction. :) Zi Song Yeoh · 4 years, 7 months ago

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@Zi Song Yeoh As Zi Song has pointed out, direct induction is one of the easiest ways to go. You can also recognize that \[a_{n} = a_{n-1} \times \left(10^{2 \cdot 3^n} + 10^{3^n} + 1 \right) = a_{n-1} \times \left( \left(10^{3^n} \right)^2 + 10^{3^n} + 1\right)\] It should be easy to show that \(3\) divides \(\left( \left(10^{3^n} \right)^2 + 10^{3^n} + 1\right)\). Hence, you can now conclude that \(3a_{n-1}\) divides \(a_n\). Marvis Narasakibma · 4 years, 7 months ago

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I came to the same solution as that of Marvis N. Question's not difficult, just presence of mind is needed! Siddharth Kumar · 4 years, 7 months ago

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this type of questions i often come across Sayan Chaudhuri · 4 years, 7 months ago

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but i think solution may be somehow critical Sayan Chaudhuri · 4 years, 7 months ago

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I DONT NOTHING ABOUT HOW TO SOLVE THIS Sayan Chaudhuri · 4 years, 7 months ago

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