List questions from divisibility

Published on 23 Apr 2019 - 5:16

83

Views

If $p$ is prime then $p^{n-1}\mid \binom{p^n}{p}$.

Published on 23 Apr 2019 - 18:46

49

Views

A problem with an infinite multitude of numbers that follow some rules

Published on 26 Mar 2026 - 15:17

307

Views

Proving or disproving $12\mid x$ given $x^2+2\mid y^2-2$

Published on 26 Mar 2026 - 14:42

177

Views

Showing that the congruum is divisible by 24

Published on 25 Mar 2026 - 21:49

304

Views

One of $a^5b-ab^5,b^5c-bc^5,c^5a-ca^5$ is divisible by $8$ if $a,b,c∈\mathbb{Z}^+$

Published on 29 Apr 2019 - 7:49

1.5k

Views

Prove that for any integer $a$, $9\nmid(a^2-3)$.

Published on 27 Mar 2026 - 19:30

304

Views

Using strong induction to prove divisibility statements

Published on 30 Apr 2019 - 3:49

1.3k

Views

Probability of ⁿC₇ being divisible by 12

Published on 30 Apr 2019 - 6:21

621

Views

If $gcd(m,n) = gcd(m,k) = gcd(n,l) =1$ show that $gcd(kn+lm, mn) = 1$

Published on 27 Mar 2026 - 5:03

108

Views

Proving that $2^{n+2} \mid a^{2^{\large{n}}} - 1 $, for $a \in \mathbb{Z}$ odd, $n \in \mathbb{N}$

Published on 01 May 2019 - 1:47

40

Views

Find $X, Y \in \mathbb{Z}$ such that $2^a X + (2^b - 1) Y = 1$ (coprimality)

Published on 23 Feb 2026 - 4:56

133

Views

Proving that $a!b!$ divides $\left(a + b \right)!$ using group theory

Published on 01 May 2019 - 11:48

73

Views

A combinatorial argument that $5$ divides $(n+2)(n+1)n(n-1)(n-2)$.

Published on 03 May 2019 - 6:29

60

Views

find some integer to make an expression an integer

Published on 03 May 2019 - 7:56

List Question

Find the smallest $n$ such that the $n$-th prime $p_n \equiv 330 \mod n $.

If $p$ is prime then $p^{n-1}\mid \binom{p^n}{p}$.

A problem with an infinite multitude of numbers that follow some rules

Proving or disproving $12\mid x$ given $x^2+2\mid y^2-2$

Showing that the congruum is divisible by 24

One of $a^5b-ab^5,b^5c-bc^5,c^5a-ca^5$ is divisible by $8$ if $a,b,c∈\mathbb{Z}^+$

Prove that for any integer $a$, $9\nmid(a^2-3)$.

Using strong induction to prove divisibility statements

Probability of ⁿC₇ being divisible by 12

If $gcd(m,n) = gcd(m,k) = gcd(n,l) =1$ show that $gcd(kn+lm, mn) = 1$

Proving that $2^{n+2} \mid a^{2^{\large{n}}} - 1 $, for $a \in \mathbb{Z}$ odd, $n \in \mathbb{N}$

Find $X, Y \in \mathbb{Z}$ such that $2^a X + (2^b - 1) Y = 1$ (coprimality)

Proving that $a!b!$ divides $\left(a + b \right)!$ using group theory

A combinatorial argument that $5$ divides $(n+2)(n+1)n(n-1)(n-2)$.

find some integer to make an expression an integer

Trending Questions

Popular # Hahtags

Popular Questions