Question

Suppose a = positive integer and gcd(a, 10) = 1. Prove that a divides infinitely many repunits.

score 523 · Answer 1 · 2019-11-10 10:03:39

523

Views

Suppose a = positive integer and gcd(a, 10) = 1. Prove that a divides infinitely many repunits.

Published on 10 Nov 2019 - 10:03

score 360 · Answer 2 · 2019-11-28 02:21:59

360

Views

Can $7$ be the smallest prime factor of a repunit?

Published on 28 Nov 2019 - 2:21

score 231 · Answer 3 · 2019-12-03 05:25:17

231

Views

Prove that there's a multiple of 1997 which has only ones in its decimal expansion

Published on 03 Dec 2019 - 5:25

score 32 · Answer 4 · 2019-12-05 16:44:12

32

Views

For a given $a$, for which values of $b$ and $c$ is the sequence $\frac{a\cdot10^n-b}{c}$ guaranteed to return integer terms with GCD=1?

Published on 05 Dec 2019 - 16:44

score 79 · Answer 5 · 2020-01-08 15:10:52

79

Views

Find the thousandth digit after the decimal point of $\sqrt N$ if N-

Published on 08 Jan 2020 - 15:10

score 39 · Answer 6 · 2020-01-27 15:11:18

39

Views

Show that if N is relatively prime to 10, then there exists a multiple that consists only of 1s.

Published on 27 Jan 2020 - 15:11

score 73 · Answer 7 · 2020-02-09 20:15:25

73

Views

How to prove statement about octal numbers

Published on 09 Feb 2020 - 20:15

score 109 · Answer 8 · 2020-02-24 13:29:11

109

Views

repeating unit of 1's

Published on 24 Feb 2020 - 13:29

score 78 · Answer 9 · 2020-03-18 13:53:29

78

Views

Number Theory Prove a complete square 1,11,111

Published on 18 Mar 2020 - 13:53

score 163 · Answer 10 · 2020-05-07 10:04:00

163

Views

School-level problem on divisibility

Published on 07 May 2020 - 10:04

score 31 · Answer 11 · 2020-05-14 15:41:00

31

Views

Pairs of Squares with repunit difference -- mistake by Selfridge and Lacampagne?

Published on 14 May 2020 - 15:41

score 428 · Answer 12 · 2020-05-15 06:00:28

428

Views

Prove that the number $ \underbrace{11 \ldots 1}_{(p-1) \mathrm{l}^{\prime} \mathrm{s}} $ is divisible by $p$

Published on 15 May 2020 - 6:00

score 733 · Answer 13 · 2020-05-25 19:10:55

733

Views

Divisibility of $a_{24}$ by 7. ($a_n=\underbrace{999\cdots9 }_{n \text{ times}})$

Published on 25 May 2020 - 19:10

score 402 · Answer 14 · 2020-07-03 08:07:01

402

Views

Prove that none of the integers $11,111,1111,...$ are squares of an integer.

Published on 03 Jul 2020 - 8:07

score 1k · Answer 15 · 2020-07-06 03:27:23

1k

Views

A positive integer has $1001$ digits all of which are $1$'s. When this number is divided by $1001$ find the remainder

Published on 06 Jul 2020 - 3:27

List Question

Suppose a = positive integer and gcd(a, 10) = 1. Prove that a divides infinitely many repunits.

Can $7$ be the smallest prime factor of a repunit?

Prove that there's a multiple of 1997 which has only ones in its decimal expansion

For a given $a$, for which values of $b$ and $c$ is the sequence $\frac{a\cdot10^n-b}{c}$ guaranteed to return integer terms with GCD=1?

Find the thousandth digit after the decimal point of $\sqrt N$ if N-

Show that if N is relatively prime to 10, then there exists a multiple that consists only of 1s.

How to prove statement about octal numbers

repeating unit of 1's

Number Theory Prove a complete square 1,11,111

School-level problem on divisibility

Pairs of Squares with repunit difference -- mistake by Selfridge and Lacampagne?

Prove that the number $ \underbrace{11 \ldots 1}_{(p-1) \mathrm{l}^{\prime} \mathrm{s}} $ is divisible by $p$

Divisibility of $a_{24}$ by 7. ($a_n=\underbrace{999\cdots9 }_{n \text{ times}})$

Prove that none of the integers $11,111,1111,...$ are squares of an integer.

A positive integer has $1001$ digits all of which are $1$'s. When this number is divided by $1001$ find the remainder

Trending Questions

Popular # Hahtags

Popular Questions