Question

Is $\frac{1}{2}(3n-2)(n-1)$ divisible by n, n+1, ..., 2n-1 if n is odd.

score 75 · Answer 1 · 2020-03-01 12:08:14

75

Views

Is $\frac{1}{2}(3n-2)(n-1)$ divisible by n, n+1, ..., 2n-1 if n is odd.

Published on 01 Mar 2020 - 12:08

score 57 · Answer 2 · 2020-03-01 15:13:54

57

Views

If $a\equiv 1\pmod {p^2},$ then $a\equiv 1\pmod p,$ for $\,a = r^{{\rm ord}(r)}$

Published on 01 Mar 2020 - 15:13

score 79 · Answer 3 · 2026-02-23 03:00:02

79

Views

Natural numbers $n$, $k$ are given such that for any prime $p$ there exists an integer $a$ satisfying the condition $p\mid a^k-n$.

Published on 23 Feb 2026 - 3:00

score 166 · Answer 4 · 2020-03-04 02:10:23

166

Views

Reshaping an object into two integer sided cuboids without changing the total volume.

Published on 04 Mar 2020 - 2:10

score 49 · Answer 5 · 2020-03-04 14:20:28

49

Views

How many solutions does $p\mid b^q-1$ have?

Published on 04 Mar 2020 - 14:20

score 235 · Answer 6 · 2026-03-25 15:44:02

235

Views

Number Theory Problem Germany 2003

Published on 25 Mar 2026 - 15:44

score 48 · Answer 7 · 2026-03-29 12:30:34

48

Views

pigeonhole principle question related to divisability

Published on 29 Mar 2026 - 12:30

score 469 · Answer 8 · 2020-03-07 23:28:04

469

Views

Prove that if $a$ is an integer, then $a(a^2+2)$ is divisible by $3$

Published on 07 Mar 2020 - 23:28

score 57 · Answer 9 · 2026-04-01 07:22:38

57

Views

Show that the function $d$ defines a metric on $\mathbb Z$.

Published on 01 Apr 2026 - 7:22

score 731 · Answer 10 · 2020-03-08 19:50:36

731

Views

Specifying a least upper bound for the number of divisors as a function of n

Published on 08 Mar 2020 - 19:50

score 77 · Answer 11 · 2020-03-10 03:40:58

77

Views

Prove that for any natural number $n$, $1000^n-1$ is not a divisor of $1978^n-1$.

Published on 10 Mar 2020 - 3:40

score 103 · Answer 12 · 2020-03-10 10:06:03

103

Views

Conflict in the definition of divisibility and definition of prime numbers?

Published on 10 Mar 2020 - 10:06

score 108 · Answer 13 · 2026-03-25 09:32:40

108

Views

Counting problem based on digital sum divisibility

Published on 25 Mar 2026 - 9:32

score 34 · Answer 14 · 2020-03-11 06:19:34

34

Views

Formula for moving object 1px when scaled down to 0.4824074074074074

Published on 11 Mar 2020 - 6:19

score 58 · Answer 15 · 2020-03-11 10:28:16

58

Views

Can every positive integer be a divisor of this sum?

Published on 11 Mar 2020 - 10:28

List Question

Is $\frac{1}{2}(3n-2)(n-1)$ divisible by n, n+1, ..., 2n-1 if n is odd.

If $a\equiv 1\pmod {p^2},$ then $a\equiv 1\pmod p,$ for $\,a = r^{{\rm ord}(r)}$

Natural numbers $n$, $k$ are given such that for any prime $p$ there exists an integer $a$ satisfying the condition $p\mid a^k-n$.

Reshaping an object into two integer sided cuboids without changing the total volume.

How many solutions does $p\mid b^q-1$ have?

Number Theory Problem Germany 2003

pigeonhole principle question related to divisability

Prove that if $a$ is an integer, then $a(a^2+2)$ is divisible by $3$

Show that the function $d$ defines a metric on $\mathbb Z$.

Specifying a least upper bound for the number of divisors as a function of n

Prove that for any natural number $n$, $1000^n-1$ is not a divisor of $1978^n-1$.

Conflict in the definition of divisibility and definition of prime numbers?

Counting problem based on digital sum divisibility

Formula for moving object 1px when scaled down to 0.4824074074074074

Can every positive integer be a divisor of this sum?

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