Question

Prove that $n^2(n^2+1)(n^2-1)$ is a multiple of $5$ for any integer $n$.

score 289 · Answer 1 · 2015-04-29 14:47:04

289

Views

Prove that $n^2(n^2+1)(n^2-1)$ is a multiple of $5$ for any integer $n$.

Published on 29 Apr 2015 - 14:47

score 346 · Answer 2 · 2026-04-11 12:18:37

346

Views

Contest Problem - Divisibility

Published on 11 Apr 2026 - 12:18

score 2.7k · Answer 3 · 2026-03-25 23:11:12

2.7k

Views

How find the fractional part of $5^{200}$ divided by $8$?

Published on 25 Mar 2026 - 23:11

score 53 · Answer 4 · 2015-05-01 16:33:49

53

Views

Analytical solution for $\max{x_1}$ in $(x_n)_{n\in\mathbb{N}}$

Published on 01 May 2015 - 16:33

score 226 · Answer 5 · 2015-05-01 18:58:06

226

Views

Proof that $(n^7-n^3)(n^5+n^3)+n^{21}-n^{13}$ is a multiple of $3$.

Published on 01 May 2015 - 18:58

score 2.2k · Answer 6 · 2015-05-02 02:26:50

2.2k

Views

Find the probability that an integer selected between 1 and 5000 is divisible by at least one of 3, 5 and 7

Published on 02 May 2015 - 2:26

score 228 · Answer 7 · 2015-05-02 12:52:53

228

Views

Find all $c\in\mathbb Z^+$ for which $\exists a,b\in\mathbb Z^+, a\neq b$ with $a+c\mid ab$ and $b+c\mid ab$

Published on 02 May 2015 - 12:52

score 41 · Answer 8 · 2026-04-11 17:45:24

41

Views

quadratic form polynomial divisibility vs. matrix pointwise multiplication.

Published on 11 Apr 2026 - 17:45

score 2.5k · Answer 9 · 2026-04-09 12:46:40

2.5k

Views

Writing a GCD of three numbers as a linear combination

Published on 09 Apr 2026 - 12:46

score 250 · Answer 10 · 2015-05-03 14:05:01

250

Views

Find GCD in Q[√3] assuming it is defined

Published on 03 May 2015 - 14:05

score 85 · Answer 11 · 2015-05-03 15:35:57

85

Views

Show that there exist $k$ and $r$ such that the given sum is divisible by $n$

Published on 03 May 2015 - 15:35

score 50 · Answer 12 · 2015-05-04 04:25:10

50

Views

Prove that if $ r,p \in \Bbb{N} $, then $ \gcd(r,rp) = r $.

Published on 04 May 2015 - 4:25

score 7.1k · Answer 13 · 2015-05-05 16:54:08

7.1k

Views

Prove the sum of any $n$ consecutive numbers is divisible by $n$ (when $n$ is odd).

Published on 05 May 2015 - 16:54

score 276 · Answer 14 · 2026-03-26 06:23:12

276

Views

Prove the existence or the non-existence of a couple of numbers ($n$,$m$) such that $n^2=m!$

Published on 26 Mar 2026 - 6:23

score 75 · Answer 15 · 2015-05-06 00:36:13

75

Views

A={n∈ℤ: 6∣n and 8∣n} and B={n∈ℤ: 48∣n}. Is A⊆B?

Published on 06 May 2015 - 0:36

List Question

Prove that $n^2(n^2+1)(n^2-1)$ is a multiple of $5$ for any integer $n$.

Contest Problem - Divisibility

How find the fractional part of $5^{200}$ divided by $8$?

Analytical solution for $\max{x_1}$ in $(x_n)_{n\in\mathbb{N}}$

Proof that $(n^7-n^3)(n^5+n^3)+n^{21}-n^{13}$ is a multiple of $3$.

Find the probability that an integer selected between 1 and 5000 is divisible by at least one of 3, 5 and 7

Find all $c\in\mathbb Z^+$ for which $\exists a,b\in\mathbb Z^+, a\neq b$ with $a+c\mid ab$ and $b+c\mid ab$

quadratic form polynomial divisibility vs. matrix pointwise multiplication.

Writing a GCD of three numbers as a linear combination

Find GCD in Q[√3] assuming it is defined

Show that there exist $k$ and $r$ such that the given sum is divisible by $n$

Prove that if $ r,p \in \Bbb{N} $, then $ \gcd(r,rp) = r $.

Prove the sum of any $n$ consecutive numbers is divisible by $n$ (when $n$ is odd).

Prove the existence or the non-existence of a couple of numbers ($n$,$m$) such that $n^2=m!$

A={n∈ℤ: 6∣n and 8∣n} and B={n∈ℤ: 48∣n}. Is A⊆B?

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