List questions from repunit-numbers

Published on 20 Aug 2013 - 22:55

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Is $\underbrace{11111\ldots1}_{91\text{ times}}$ a prime number?

Published on 12 May 2017 - 10:02

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If $11..11$($n$ times 1) is prime, prove that $n$ is also prime

Published on 14 Jul 2017 - 18:29

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Why primes $\neq 2,5$ divide infinitely many repunits? (cyclic permutation orbits)

Published on 16 Sep 2010 - 6:59

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Prove that every number ending in a $3$ has a multiple which consists only of ones.

Published on 27 Jun 2012 - 14:02

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Prove that none of $\{11, 111, 1111,\dots \}$ is the perfect square of an integer

Published on 08 Feb 2013 - 19:22

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When is the number $11111\cdots1$ a prime number?

Published on 12 Feb 2013 - 1:51

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Prove that $11,111,111.....$ is not a perfect square

Published on 12 Aug 2020 - 3:06

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Finding the number of digits in repunit

Published on 13 Sep 2020 - 4:51

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Are there any solutions to this nonlinear diophantine equation?

Published on 23 Feb 2026 - 7:43

132

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Doubt about whether repunits are square

Published on 09 Oct 2020 - 16:18

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Show that the integers 1111, 111111, 11111111, ... (numbers formed by an even number of numbers 1) are all composed.

Published on 20 Nov 2020 - 20:42

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Let $a_n = 1 . . . 1 $ with $3^n$ digits. Prove that $a_n$ is divisible by $3a_{n−1}$.

Published on 15 Dec 2020 - 18:48

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A similar (little) Fermat's Theorem result and repunit multiple

Published on 07 Jan 2021 - 23:22

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Prime Repunit Numbers

Published on 21 Feb 2021 - 13:58

List Question

Repunit Divisibility

Is $\underbrace{11111\ldots1}_{91\text{ times}}$ a prime number?

If $11..11$($n$ times 1) is prime, prove that $n$ is also prime

Why primes $\neq 2,5$ divide infinitely many repunits? (cyclic permutation orbits)

Prove that every number ending in a $3$ has a multiple which consists only of ones.

Prove that none of $\{11, 111, 1111,\dots \}$ is the perfect square of an integer

When is the number $11111\cdots1$ a prime number?

Prove that $11,111,111.....$ is not a perfect square

Finding the number of digits in repunit

Are there any solutions to this nonlinear diophantine equation?

Doubt about whether repunits are square

Show that the integers 1111, 111111, 11111111, ... (numbers formed by an even number of numbers 1) are all composed.

Let $a_n = 1 . . . 1 $ with $3^n$ digits. Prove that $a_n$ is divisible by $3a_{n−1}$.

A similar (little) Fermat's Theorem result and repunit multiple

Prime Repunit Numbers

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