Question

Let $t$ be a positive real number. Prove that there is a positive integer $n$ such that the decimal expansion of $nt$ contains a $7$.

score 26 · Answer 1 · 2023-07-05 05:01:54

Let $t$ be a positive real number. Prove that there is a positive integer $n$ such that the decimal expansion of $nt$ contains a $7$.

score 106 · Answer 2 · 2023-07-05 10:09:58

106

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Find the smallest positive multiple of $1999$ that ends in $2006$ (last four digits)

Published on 05 Jul 2023 - 10:09

score 152 · Answer 3 · 2023-07-06 06:40:05

152

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Perfect square in the sequence formed by consecutive numbers

Published on 06 Jul 2023 - 6:40

score 36 · Answer 4 · 2026-02-23 22:50:11

36

Views

Proportion of a digit in an algebraic number's binary expansion

Published on 23 Feb 2026 - 22:50

score 308 · Answer 5 · 2023-07-09 15:14:51

308

Views

What numbers have a multiple that in base 10, can be written with only the digits $2$ and $5$.

Published on 09 Jul 2023 - 15:14

score 29 · Answer 6 · 2026-03-27 07:49:11

29

Views

To prove that the Cantor function maps the end points of the intervals removed to a same point

Published on 27 Mar 2026 - 7:49

score 834 · Answer 7 · 2026-03-25 22:10:53

834

Views

Is there any perfect power in the sequence $12,123,1234,12345,...$?

Published on 25 Mar 2026 - 22:10

score 172 · Answer 8 · 2026-02-23 05:17:16

172

Views

Is there a third Carmichael number with only odd digits?

Published on 23 Feb 2026 - 5:17

score 85 · Answer 9 · 2023-07-21 05:14:01

85

Views

Prove that This Property Does Not Hold for Any Other Pair of Digits.

Published on 21 Jul 2023 - 5:14

score 162 · Answer 10 · 2023-07-21 17:34:20

162

Views

Numbers such that $(\overline{a_1\dots a_n})^2=\overline{x_1\dots x_m}$ and $(\overline{a_n\dots a_1})^2=\overline{x_m\dots x_1}$.

Published on 21 Jul 2023 - 17:34

score 39 · Answer 11 · 2026-02-23 05:09:51

39

Views

Carmichael-numbers with only one odd digit

Published on 23 Feb 2026 - 5:09

score 222 · Answer 12 · 2023-07-31 00:11:28

222

Views

How many subsets of $\{0,1,2,3,4,5,6,7,8,9\}$ could be realized as the set of distinct digits of a prime?

Published on 31 Jul 2023 - 0:11

score 97 · Answer 13 · 2023-08-04 15:35:44

97

Views

What is the measure of the set of numbers in $[0,1]$ whose digits have a mean of $0$?

Published on 04 Aug 2023 - 15:35

score 47 · Answer 14 · 2023-08-09 12:51:02

47

Views

If $\{n_k\}$ is the set of natural numbers with no 0 in their decimal expansion, $\sum_{k=1}^\infty \frac{1}{n_k}$ converges to a number less than 90

Published on 09 Aug 2023 - 12:51

score 31 · Answer 15 · 2023-08-10 11:03:57

31

Views

two forms of infinite decimal which are rewritten from finite decimal

Published on 10 Aug 2023 - 11:03

List Question

Let $t$ be a positive real number. Prove that there is a positive integer $n$ such that the decimal expansion of $nt$ contains a $7$.

Find the smallest positive multiple of $1999$ that ends in $2006$ (last four digits)

Perfect square in the sequence formed by consecutive numbers

Proportion of a digit in an algebraic number's binary expansion

What numbers have a multiple that in base 10, can be written with only the digits $2$ and $5$.

To prove that the Cantor function maps the end points of the intervals removed to a same point

Is there any perfect power in the sequence $12,123,1234,12345,...$?

Is there a third Carmichael number with only odd digits?

Prove that This Property Does Not Hold for Any Other Pair of Digits.

Numbers such that $(\overline{a_1\dots a_n})^2=\overline{x_1\dots x_m}$ and $(\overline{a_n\dots a_1})^2=\overline{x_m\dots x_1}$.

Carmichael-numbers with only one odd digit

How many subsets of $\{0,1,2,3,4,5,6,7,8,9\}$ could be realized as the set of distinct digits of a prime?

What is the measure of the set of numbers in $[0,1]$ whose digits have a mean of $0$?

If $\{n_k\}$ is the set of natural numbers with no 0 in their decimal expansion, $\sum_{k=1}^\infty \frac{1}{n_k}$ converges to a number less than 90

two forms of infinite decimal which are rewritten from finite decimal

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