Question

Determine a property of $S_b(n)$, which is the sum of the digits of $n$ when $n$ is expressed in base $b$

score 227 · Answer 1 · 2026-03-25 12:49:41

227

Views

Determine a property of $S_b(n)$, which is the sum of the digits of $n$ when $n$ is expressed in base $b$

Published on 25 Mar 2026 - 12:49

score 188 · Answer 2 · 2019-04-08 19:08:50

188

Views

Are are infinitely many intimate pairs of integers?

Published on 08 Apr 2019 - 19:08

score 252 · Answer 3 · 2019-04-11 13:30:44

252

Views

Find all pairs $(m, n)$ of positive integers such that $m$ divides $8n+1$ and $n$ divides $8m+1$

Published on 11 Apr 2019 - 13:30

score 712 · Answer 4 · 2019-04-12 06:19:35

712

Views

If $y^2-x^2\bigm|2^ky-1$ and $2^k-1\bigm|y-1$ then $y=2^k$ and $x=1$

Published on 12 Apr 2019 - 6:19

score 222 · Answer 5 · 2019-04-12 11:38:26

222

Views

$K\mid\frac{N}J\iff J\mid\frac{N}K\ $ [Divisor Reciprocity]

Published on 12 Apr 2019 - 11:38

score 182 · Answer 6 · 2019-04-13 11:43:16

182

Views

Number of divisors of $ 20^{20} $ with exactly $20$ divisors

Published on 13 Apr 2019 - 11:43

score 28 · Answer 7 · 2019-04-15 13:43:27

28

Views

Return the number of integers within the range of a and b that are divisible by x

Published on 15 Apr 2019 - 13:43

score 260 · Answer 8 · 2019-04-15 19:00:06

260

Views

Show that $(\binom{p^2}{p} -p ) $ is divisible by $p^5$, for every prime number $p, p\ge 5$

Published on 15 Apr 2019 - 19:00

score 188 · Answer 9 · 2019-04-16 09:43:14

188

Views

Two friends have $2$ natural written on their forehead. One is $2$ times the other + $1$. They can raise their hands.

Published on 16 Apr 2019 - 9:43

score 113 · Answer 10 · 2019-04-16 15:21:03

113

Views

Does there exist a composite, deficient, odd number that is divisible by the sum of its proper factors?

Published on 16 Apr 2019 - 15:21

score 130 · Answer 11 · 2019-04-16 16:45:07

130

Views

Elementary number theory proofs

Published on 16 Apr 2019 - 16:45

score 119 · Answer 12 · 2019-04-18 13:47:51

119

Views

Divisibility of $x^2+y^2$ by prime $p$

Published on 18 Apr 2019 - 13:47

score 63 · Answer 13 · 2019-04-19 12:54:17

63

Views

I am looking for a proof of a certain set being divisible by 7

Published on 19 Apr 2019 - 12:54

score 91 · Answer 14 · 2026-03-25 21:45:59

91

Views

Perfect squares and divisor

Published on 25 Mar 2026 - 21:45

score 32 · Answer 15 · 2026-03-27 16:26:30

32

Views

Divisor Properties

Published on 27 Mar 2026 - 16:26

List Question

Determine a property of $S_b(n)$, which is the sum of the digits of $n$ when $n$ is expressed in base $b$

Are are infinitely many intimate pairs of integers?

Find all pairs $(m, n)$ of positive integers such that $m$ divides $8n+1$ and $n$ divides $8m+1$

If $y^2-x^2\bigm|2^ky-1$ and $2^k-1\bigm|y-1$ then $y=2^k$ and $x=1$

$K\mid\frac{N}J\iff J\mid\frac{N}K\ $ [Divisor Reciprocity]

Number of divisors of $ 20^{20} $ with exactly $20$ divisors

Return the number of integers within the range of a and b that are divisible by x

Show that $(\binom{p^2}{p} -p ) $ is divisible by $p^5$, for every prime number $p, p\ge 5$

Two friends have $2$ natural written on their forehead. One is $2$ times the other + $1$. They can raise their hands.

Does there exist a composite, deficient, odd number that is divisible by the sum of its proper factors?

Elementary number theory proofs

Divisibility of $x^2+y^2$ by prime $p$

I am looking for a proof of a certain set being divisible by 7

Perfect squares and divisor

Divisor Properties

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