Question

Smallest $n$-digit number $x$ with cyclic permutations multiples of $1989$

score 158 · Answer 1 · 2026-04-13 21:08:26

158

Views

Smallest $n$-digit number $x$ with cyclic permutations multiples of $1989$

Published on 13 Apr 2026 - 21:08

score 482 · Answer 2 · 2026-04-14 01:30:16

482

Views

Can exist an even number greater than $36$ with more even divisors than $36$, all of them being a prime$-1$?

Published on 14 Apr 2026 - 1:30

score 546 · Answer 3 · 2026-04-13 21:50:01

546

Views

Relation of divisibility - hasse diagram

Published on 13 Apr 2026 - 21:50

score 314 · Answer 4 · 2026-04-12 15:06:39

314

Views

is $7^{101} + 18^{101}$ divisible by $25$?

Published on 12 Apr 2026 - 15:06

score 10.8k · Answer 5 · 2016-01-08 12:09:48

10.8k

Views

Find all $n$ such that $3^{2n+1}+2^{n+2}$ is divisible by $7$

Published on 08 Jan 2016 - 12:09

score 199 · Answer 6 · 2026-04-04 10:17:37

199

Views

Prove: $\forall$ $n\in \mathbb N, (2^n)!$ is divisible by $2^{(2^n)-1}$ and is not divisible by $2^{2^n}$

Published on 04 Apr 2026 - 10:17

score 141 · Answer 7 · 2026-03-29 04:10:53

141

Views

Dilemma about the value of $\frac{4- 4}{4 - 4}$

Published on 29 Mar 2026 - 4:10

score 97 · Answer 8 · 2026-03-27 03:43:15

97

Views

Prove that $τ(m^n)$ and $n$ are coprime $(m,n ∈ N^+)$

Published on 27 Mar 2026 - 3:43

score 1k · Answer 9 · 2026-03-26 06:31:43

1k

Views

Prove that ($\frac{-2}{p}$)= 1 if and only if p is of the form $8k + 1$ or $8k + 3$

Published on 26 Mar 2026 - 6:31

score 121 · Answer 10 · 2016-01-10 19:07:32

121

Views

If $a^n+n^b\mid c^n+n^d$ for every $n$ then $c=a^k$ and $d=kb$ .

Published on 10 Jan 2016 - 19:07

score 79 · Answer 11 · 2026-04-04 12:00:10

79

Views

Problem on factorials and divisiblity of number theory

Published on 04 Apr 2026 - 12:00

score 187 · Answer 12 · 2026-04-07 15:40:04

187

Views

Prove that $(a-b)^n\mid (a^n-b^n) \iff n=1$ under given conditions

Published on 07 Apr 2026 - 15:40

score 62 · Answer 13 · 2026-04-14 08:50:36

62

Views

$\exists\ n \gt 34131$ with more than $7$ odd divisors $d_i \gt 1$ such as when $d_i+1$ are accumulated in increasing order to $1$ the sums are prime?

Published on 14 Apr 2026 - 8:50

score 403 · Answer 14 · 2026-04-13 17:10:14

403

Views

If n is positive integer, prove that the prime factorization of $2^{2n}\times 3^n - 1$ contains $11$ as one of the prime factors

Published on 13 Apr 2026 - 17:10

score 92 · Answer 15 · 2016-01-12 08:32:25

92

Views

Without using prime factorization, show if $m\mid n^2$ then $\gcd(m,n^2/m)\mid n$

Published on 12 Jan 2016 - 8:32

List Question

Smallest $n$-digit number $x$ with cyclic permutations multiples of $1989$

Can exist an even number greater than $36$ with more even divisors than $36$, all of them being a prime$-1$?

Relation of divisibility - hasse diagram

is $7^{101} + 18^{101}$ divisible by $25$?

Find all $n$ such that $3^{2n+1}+2^{n+2}$ is divisible by $7$

Prove: $\forall$ $n\in \mathbb N, (2^n)!$ is divisible by $2^{(2^n)-1}$ and is not divisible by $2^{2^n}$

Dilemma about the value of $\frac{4- 4}{4 - 4}$

Prove that $τ(m^n)$ and $n$ are coprime $(m,n ∈ N^+)$

Prove that ($\frac{-2}{p}$)= 1 if and only if p is of the form $8k + 1$ or $8k + 3$

If $a^n+n^b\mid c^n+n^d$ for every $n$ then $c=a^k$ and $d=kb$ .

Problem on factorials and divisiblity of number theory

Prove that $(a-b)^n\mid (a^n-b^n) \iff n=1$ under given conditions

$\exists\ n \gt 34131$ with more than $7$ odd divisors $d_i \gt 1$ such as when $d_i+1$ are accumulated in increasing order to $1$ the sums are prime?

If n is positive integer, prove that the prime factorization of $2^{2n}\times 3^n - 1$ contains $11$ as one of the prime factors

Without using prime factorization, show if $m\mid n^2$ then $\gcd(m,n^2/m)\mid n$

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