Question

Finding a contradiction for analysis problem

score 49 · Answer 1 · 2020-07-17 09:30:40

49

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Finding a contradiction for analysis problem

Published on 17 Jul 2020 - 9:30

score 180 · Answer 2 · 2026-04-02 15:54:17

180

Views

Do there exist any three relatively prime natural numbers so that the square of each of them is divisible by the sum of the two remaining numbers?

Published on 02 Apr 2026 - 15:54

score 76 · Answer 3 · 2026-04-01 09:50:28

76

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Integer exponent equation

Published on 01 Apr 2026 - 9:50

score 45 · Answer 4 · 2026-03-28 12:14:06

45

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Solution verification: Harmonic polynomial $p \in \mathbb{R}[x_1, \dots, x_n]$ divisible by $x_1^2+\dots+x_n^2$ must be identically $0.$

Published on 28 Mar 2026 - 12:14

score 57 · Answer 5 · 2026-03-29 21:58:15

57

Views

How to prove it is a perfect-square.

Published on 29 Mar 2026 - 21:58

score 400 · Answer 6 · 2026-03-25 10:53:00

400

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Can I efficiently find the divisors nearest to the square-root?

Published on 25 Mar 2026 - 10:53

score 883 · Answer 7 · 2020-07-21 05:33:51

883

Views

How do I use structural induction to show that for all $(a,b) \in S$ that $(a+b) = 4k$ for some $k \in \Bbb Z$?

Published on 21 Jul 2020 - 5:33

score 310 · Answer 8 · 2020-07-21 20:01:12

310

Views

What should $n$ be equal to, so that $5^{2n+1}2^{n+2} + 3^{n+2}2^{2n+1}$ is completely divisible by $19$?

Published on 21 Jul 2020 - 20:01

score 95 · Answer 9 · 2020-07-22 03:22:21

95

Views

Prove or disprove that If $a\mid c$ and $b\mid c$, then $ab \mid c$.

Published on 22 Jul 2020 - 3:22

score 63 · Answer 10 · 2020-07-22 11:54:35

63

Views

Is it always possible to prove a divisibility question using combinatorial argument?

Published on 22 Jul 2020 - 11:54

score 107 · Answer 11 · 2026-03-30 17:54:43

107

Views

Remainder when $^{40}C_{12}$ is divided by $7$.

Published on 30 Mar 2026 - 17:54

score 1.7k · Answer 12 · 2020-07-24 04:03:21

1.7k

Views

Prove that $5^{3^n} + 1$ is divisible by $3^{n + 1}$ for all nonnegative integers $n.$

Published on 24 Jul 2020 - 4:03

score 53 · Answer 13 · 2020-07-24 20:05:08

53

Views

Establishing divisibility by a prime

Published on 24 Jul 2020 - 20:05

score 49 · Answer 14 · 2020-07-24 22:48:12

49

Views

When is $\sum_{i=1}^{m}i^n =0 \bmod \dfrac{m(m+1)}{2}$?

Published on 24 Jul 2020 - 22:48

score 58 · Answer 15 · 2020-07-25 04:40:39

58

Views

True or false questions about divisibility and non-divisibility in the integers. I'm confused.

Published on 25 Jul 2020 - 4:40

List Question

Finding a contradiction for analysis problem

Do there exist any three relatively prime natural numbers so that the square of each of them is divisible by the sum of the two remaining numbers?

Integer exponent equation

Solution verification: Harmonic polynomial $p \in \mathbb{R}[x_1, \dots, x_n]$ divisible by $x_1^2+\dots+x_n^2$ must be identically $0.$

How to prove it is a perfect-square.

Can I efficiently find the divisors nearest to the square-root?

How do I use structural induction to show that for all $(a,b) \in S$ that $(a+b) = 4k$ for some $k \in \Bbb Z$?

What should $n$ be equal to, so that $5^{2n+1}2^{n+2} + 3^{n+2}2^{2n+1}$ is completely divisible by $19$?

Prove or disprove that If $a\mid c$ and $b\mid c$, then $ab \mid c$.

Is it always possible to prove a divisibility question using combinatorial argument?

Remainder when $^{40}C_{12}$ is divided by $7$.

Prove that $5^{3^n} + 1$ is divisible by $3^{n + 1}$ for all nonnegative integers $n.$

Establishing divisibility by a prime

When is $\sum_{i=1}^{m}i^n =0 \bmod \dfrac{m(m+1)}{2}$?

True or false questions about divisibility and non-divisibility in the integers. I'm confused.

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