Let a n denote the n-digit positive integer 11 ⋯ 1 (a string of n ones). Which statements hold?

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Mathematics - Sequence & Series Question with Solution | TestHub

MathematicsSequence & SeriesSpecial sequences/seriesMedium2 minQB

MathematicsMediummultiple choice

Let $a_{n}$ denote the n-digit positive integer $11 \dots 1$ (a string of n ones). Which statements hold?

Options:(select one or more)

Answer:

A, B, C, D

Solution:

The first three lengths are divisible by 3, so their repunits are divisible by the nontrivial factor $a_{3} = 111$ . Since $91 = 7 \cdot 13, a_{91}$ is divisible by the nontrivial repunit $a_{7}$ .

Stream:JEESubject:MathematicsTopic:Sequence & SeriesSubtopic:Special sequences/series

⏱ 2mℹ️ Source: QB

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