List questions from divisibility

Published on 08 Apr 2026 - 10:14

914

Views

prove that there are infinitely many numbers of the form $x = 111....1$ such that $31\mid x$

Published on 09 Apr 2026 - 16:44

176

Views

Prove that for any positive integer $n$ the number $1 - {n \choose 2}a + {n \choose 4}a^2 - {n \choose 6}a^3+\cdots$ is divisible by $2^{n-1}$.

Published on 14 Jun 2015 - 14:01

94

Views

If $a\mid b+c$ and $\gcd(b,c)=1$, prove $\gcd(a,b)=\gcd(a,c)=1$

Published on 02 Apr 2026 - 23:19

100

Views

If $a\mid b$ then $\gcd(a,c) \leq \gcd(b,c)$

Published on 14 Jun 2015 - 21:30

33

Views

Divisibiltiy of the order of elements in a group

Published on 16 Jun 2015 - 8:01

791

Views

If $\gcd(a,4)=\gcd(b,4)=2$, find $\gcd(a+b,4)$.

Published on 02 Apr 2026 - 23:25

1k

Views

Decimal/hex palindromes: why multiples of 53?

Published on 25 Mar 2026 - 13:54

341

Views

Determining if all integers of the polynomial form $n^2+21n+1$ are prime

Published on 30 Mar 2026 - 14:43

149

Views

Show that $\prod _{i<j}(x_i-x_j)$ can be divided wihout remainder in $\prod_{i<j}(i-j)$

Published on 01 Apr 2026 - 16:57

288

Views

Divisibility of a polynomial by another polynomial

Published on 10 Apr 2026 - 15:43

53

Views

A number root of two irreducible polynomials?

Published on 18 Jun 2015 - 14:38

7.8k

Views

Find the sum of reciprocals of divisors given the sum of divisors

Published on 11 Apr 2026 - 23:18

3k

Views

$p$ divides $n^p-n$

Published on 19 Jun 2015 - 18:25

100

Views

Example of binary GCD for complex integers?

Published on 02 Apr 2026 - 23:24

List Question

Finding solutions to a symmetric divisibility condition $x\mid p(y),\;y\mid p(x)$

prove that there are infinitely many numbers of the form $x = 111....1$ such that $31\mid x$

Prove that for any positive integer $n$ the number $1 - {n \choose 2}a + {n \choose 4}a^2 - {n \choose 6}a^3+\cdots$ is divisible by $2^{n-1}$.

If $a\mid b+c$ and $\gcd(b,c)=1$, prove $\gcd(a,b)=\gcd(a,c)=1$

If $a\mid b$ then $\gcd(a,c) \leq \gcd(b,c)$

Divisibiltiy of the order of elements in a group

If $\gcd(a,4)=\gcd(b,4)=2$, find $\gcd(a+b,4)$.

Decimal/hex palindromes: why multiples of 53?

Determining if all integers of the polynomial form $n^2+21n+1$ are prime

Show that $\prod _{i<j}(x_i-x_j)$ can be divided wihout remainder in $\prod_{i<j}(i-j)$

Divisibility of a polynomial by another polynomial

A number root of two irreducible polynomials?

Find the sum of reciprocals of divisors given the sum of divisors

$p$ divides $n^p-n$

Example of binary GCD for complex integers?

Trending Questions

Popular # Hahtags

Popular Questions