List questions from divisibility

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Prove $x^3-3x+4$ is irreducible in $\mathbb{Q}[x]$

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GCD of two real numbers

Published on 31 Mar 2014 - 15:51

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What is the remainder when 4 to the power 1000 is divided by 7

Published on 01 Apr 2014 - 14:19

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My first proof that uses the well-ordering principle (very simple number theory). Please mark/grade.

Published on 02 Apr 2014 - 5:49

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Please help to prove the following.

Published on 02 Apr 2014 - 16:26

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Proof of $(ma+ nb, mn)=(a,n)(b,m)$

Published on 02 Apr 2014 - 23:07

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How multiple of number is determined?

Published on 03 Apr 2014 - 6:41

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if $gcd(a,b)=gcd(a,b,c)$ then I need to prove that $ax+by=c$ has solution in $\mathbb Z$

Published on 03 Apr 2014 - 13:42

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Prove that if $d|a$, then $d||a|$

Published on 03 Apr 2014 - 15:05

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What is the best way of solving for $x,y\in\mathbb N$ given the conditions $\begin{cases}x\mid y+a\\y\mid x + b\end{cases}$?

Published on 29 Mar 2026 - 14:35

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Solving a divisibility problem using group theory

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find all the divisors of $6$ and $4+2\sqrt{5}$,then find $\gcd(6,4+2\sqrt{5})$

Published on 05 Apr 2014 - 15:12

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Why if $a = qb + r$, then $\operatorname{gcd}(a,b) = \operatorname{gcd}(b, r)$ intuitively?

Published on 27 Mar 2026 - 21:19

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Find integers $k$ and $l$ such that $\gcd(-5775,-651)$ can be expressed in the form $ka + bl$

Published on 06 Apr 2014 - 19:30

List Question

GCD for multivariable polynomial ring

Prove $x^3-3x+4$ is irreducible in $\mathbb{Q}[x]$

GCD of two real numbers

What is the remainder when 4 to the power 1000 is divided by 7

My first proof that uses the well-ordering principle (very simple number theory). Please mark/grade.

Please help to prove the following.

Proof of $(ma+ nb, mn)=(a,n)(b,m)$

How multiple of number is determined?

if $gcd(a,b)=gcd(a,b,c)$ then I need to prove that $ax+by=c$ has solution in $\mathbb Z$

Prove that if $d|a$, then $d||a|$

What is the best way of solving for $x,y\in\mathbb N$ given the conditions $\begin{cases}x\mid y+a\\y\mid x + b\end{cases}$?

Solving a divisibility problem using group theory

find all the divisors of $6$ and $4+2\sqrt{5}$,then find $\gcd(6,4+2\sqrt{5})$

Why if $a = qb + r$, then $\operatorname{gcd}(a,b) = \operatorname{gcd}(b, r)$ intuitively?

Find integers $k$ and $l$ such that $\gcd(-5775,-651)$ can be expressed in the form $ka + bl$

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