Question

Conjecture: $\prod\limits_{k=0}^{n}\binom{2n}{k}$ is divisible by $\prod\limits_{k=0}^n\binom{2k}{k}$ only if $n=1,2,5$.

score 131 · Answer 1 · 2026-03-28 12:14:26

131

Views

Conjecture: $\prod\limits_{k=0}^{n}\binom{2n}{k}$ is divisible by $\prod\limits_{k=0}^n\binom{2k}{k}$ only if $n=1,2,5$.

Published on 28 Mar 2026 - 12:14

score 20 · Answer 2 · 2023-12-05 20:43:02

20

Views

Let A' be obtained from A by gauss' reduction; what can we say about their determinants?

Published on 05 Dec 2023 - 20:43

score 59 · Answer 3 · 2026-04-02 10:45:30

59

Views

Condition for No Solution in Dividing Apples Equally Among People

Published on 02 Apr 2026 - 10:45

score 32 · Answer 4 · 2023-12-15 13:37:27

32

Views

Pattern in the universal divisibility test

Published on 15 Dec 2023 - 13:37

score 40 · Answer 5 · 2026-03-28 23:59:59

40

Views

Vinogradov's proof that $U_{p^{\alpha}}$ is cyclic. How to prove $p^{r-1} (p-1) \mid \delta$ for $1 \leq r \leq \alpha$

Published on 28 Mar 2026 - 23:59

score 51 · Answer 6 · 2023-12-28 07:18:13

51

Views

Does the result given below work for composite numbers?

Published on 28 Dec 2023 - 7:18

score 120 · Answer 7 · 2023-12-28 19:22:45

120

Views

Find pairwise coprime $a$ $b$ $c$ with certain property

Published on 28 Dec 2023 - 19:22

score 133 · Answer 8 · 2023-12-29 10:26:42

133

Views

Finding the lowest value of m that is greater than 2 in $m^3-3m^2+2m$ which is divisible by both 79 and 83

Published on 29 Dec 2023 - 10:26

score 21 · Answer 9 · 2023-12-30 05:23:00

21

Views

Prove divisibilty through inequality

Published on 30 Dec 2023 - 5:23

score 72 · Answer 10 · 2023-12-31 04:15:58

72

Views

Prove that $n$ is the median of all positive divisor of $n^2$ for any positive integer $n$.

Published on 31 Dec 2023 - 4:15

score 245 · Answer 11 · 2023-12-31 11:53:33

245

Views

Find all positive integers $n$ such that $n$ divides $9^{n-1}+3^{n-1}+1$.

Published on 31 Dec 2023 - 11:53

score 258 · Answer 12 · 2024-01-03 22:53:39

258

Views

How to show relation between squarefree sets

Published on 03 Jan 2024 - 22:53

score 137 · Answer 13 · 2024-01-05 13:16:30

137

Views

If $p,q$ are primes, and $p>q>5$, prove that $240\vert p^4 - q^4$

Published on 05 Jan 2024 - 13:16

score 868 · Answer 14 · 2024-01-07 02:34:15

868

Views

Is $\frac{(p-1)^p+1}{p^2}$ square-free?

Published on 07 Jan 2024 - 2:34

score 72 · Answer 15 · 2024-01-07 17:17:56

72

Views

Divisibility algorithm for all prime number

Published on 07 Jan 2024 - 17:17

List Question

Conjecture: $\prod\limits_{k=0}^{n}\binom{2n}{k}$ is divisible by $\prod\limits_{k=0}^n\binom{2k}{k}$ only if $n=1,2,5$.

Let A' be obtained from A by gauss' reduction; what can we say about their determinants?

Condition for No Solution in Dividing Apples Equally Among People

Pattern in the universal divisibility test

Vinogradov's proof that $U_{p^{\alpha}}$ is cyclic. How to prove $p^{r-1} (p-1) \mid \delta$ for $1 \leq r \leq \alpha$

Does the result given below work for composite numbers?

Find pairwise coprime $a$ $b$ $c$ with certain property

Finding the lowest value of m that is greater than 2 in $m^3-3m^2+2m$ which is divisible by both 79 and 83

Prove divisibilty through inequality

Prove that $n$ is the median of all positive divisor of $n^2$ for any positive integer $n$.

Find all positive integers $n$ such that $n$ divides $9^{n-1}+3^{n-1}+1$.

How to show relation between squarefree sets

If $p,q$ are primes, and $p>q>5$, prove that $240\vert p^4 - q^4$

Is $\frac{(p-1)^p+1}{p^2}$ square-free?

Divisibility algorithm for all prime number

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