List questions from divisibility

Published on 29 Mar 2026 - 4:42

137

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Prove $(n!-1,(n-1)!-1)=1$

Published on 05 Feb 2015 - 12:46

272

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Which subrings $S$ of $\mathbb Z_n$contains a multiplicative identity , that is $\exists e\in S$ such that for every $x \in S , x.e=e.x=x$ ?

Published on 29 Mar 2026 - 0:00

31

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Use the euclidean algorithm to prove that if gcd(a,b) = 1 and a|c and b|c then ab|c

Published on 05 Feb 2015 - 22:08

657

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Can we prove the existence of a gcd in $\mathbb Z$ without using division with remainder?

Published on 08 Apr 2026 - 20:44

2.7k

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Show that $\rm lcm(a,b)=ab \iff gcd(a,b)=1$

Published on 23 Feb 2026 - 21:36

839

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Divisor of a product of integers is a product of divisors

Published on 02 Apr 2026 - 17:44

134

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Induction divisibility proof

Published on 07 Feb 2015 - 11:38

405

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To prove ${2p - 1 \choose p } \equiv 1 \pmod{p^2}$ without using Wolstenholme's theorem

Published on 28 Mar 2026 - 22:28

128

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$f,g,h$ are polynomials. Show that....

Published on 08 Feb 2015 - 10:03

97

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How can I show that $(x-1)(x^2-1)$ divides the polynomial $(x^n-1)(x^{n+1}-1)$?

Published on 09 Apr 2026 - 2:37

112

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If $n^m\mid m^n$ and $k^n\mid n^k$, prove $k^m\mid m^k$, $m,n,k\in \mathbb{Z}^+$

Published on 08 Feb 2015 - 16:20

105

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If $a,b,c\neq0$, prove that $ac\mid bc \iff a\mid b$

Published on 08 Feb 2015 - 16:40

1.1k

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Show that $A[X]/(aX+b)$ is an integral domain

Published on 27 Mar 2026 - 2:39

2.7k

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Proof that if x is prime, then x+7 is composite.

Published on 08 Feb 2015 - 22:39

List Question

Long division to primitive roots?

Prove $(n!-1,(n-1)!-1)=1$

Which subrings $S$ of $\mathbb Z_n$contains a multiplicative identity , that is $\exists e\in S$ such that for every $x \in S , x.e=e.x=x$ ?

Use the euclidean algorithm to prove that if gcd(a,b) = 1 and a|c and b|c then ab|c

Can we prove the existence of a gcd in $\mathbb Z$ without using division with remainder?

Show that $\rm lcm(a,b)=ab \iff gcd(a,b)=1$

Divisor of a product of integers is a product of divisors

Induction divisibility proof

To prove ${2p - 1 \choose p } \equiv 1 \pmod{p^2}$ without using Wolstenholme's theorem

$f,g,h$ are polynomials. Show that....

How can I show that $(x-1)(x^2-1)$ divides the polynomial $(x^n-1)(x^{n+1}-1)$?

If $n^m\mid m^n$ and $k^n\mid n^k$, prove $k^m\mid m^k$, $m,n,k\in \mathbb{Z}^+$

If $a,b,c\neq0$, prove that $ac\mid bc \iff a\mid b$

Show that $A[X]/(aX+b)$ is an integral domain

Proof that if x is prime, then x+7 is composite.

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