Newbetuts

Let $a,m,n \in \mathbf{N}$. Show that if $\gcd(m,n)=1$, then $\gcd(a,mn)=\gcd(a,m)\cdot\gcd(a,n)$. [duplicate]

What is the difference between Euclid's division lemma and Euclid's division algorithm?

Can the determinant of an integer matrix with a given row be any multiple of the gcd of that row?

Why does the Euclidean algorithm for finding GCD work?

Prove $\gcd(a+b,a^2+b^2)$ is $1$ or $2$ if $\gcd(a,b) = 1$

If the sum of positive integers $a$ and $b$ is a prime, their gcd is $1$. Proof?

Prove that $\gcd(a+b,\text{lcm}(a,b))=\gcd(a,b)$ where $a,b\in\mathbb{Z}$. [duplicate]

Prove that $\gcd(3^n-2,2^n-3)=\gcd(5,2^n-3)$

Zagiers Class Number Definition of Binary Quadratic Forms

On odd perfect numbers and a GCD - Part V

Is there an Integral domain that is a GCD domain but NOT a UFD? [duplicate]

Show that any two consecutive odd integers are relatively prime

On odd perfect numbers and a GCD - Part VI

If $N = q^k n^2$ is an odd perfect number with special prime $q$, then can $N$ be of the form $q^k \cdot (\sigma(q^k)/2) \cdot {n}$?

Let $a\mid c$ and $b\mid c$ such that $\gcd(a,b)=1$, Show that $ab\mid c$

New posts in gcd-and-lcm

Inductive proof of gcd Bezout identity (from Apostol: Math, Analysis 2ed)

Show that if $(b,c)=1$, then $(a,bc)=(a,b)(a,c)$.

Proving that $a,n$ and $b, n$ relatively prime implies $ab,n$ relatively prime

Should a polynomial satisfying certain conditions be linear?

Prove that $\gcd(n!+1,(n+1)!+1)=1$

Let $a,m,n \in \mathbf{N}$. Show that if $\gcd(m,n)=1$, then $\gcd(a,mn)=\gcd(a,m)\cdot\gcd(a,n)$. [duplicate]

What is the difference between Euclid's division lemma and Euclid's division algorithm?

Can the determinant of an integer matrix with a given row be any multiple of the gcd of that row?

Why does the Euclidean algorithm for finding GCD work?

Prove $\gcd(a+b,a^2+b^2)$ is $1$ or $2$ if $\gcd(a,b) = 1$

If the sum of positive integers $a$ and $b$ is a prime, their gcd is $1$. Proof?

Prove that $\gcd(a+b,\text{lcm}(a,b))=\gcd(a,b)$ where $a,b\in\mathbb{Z}$. [duplicate]

Prove that $\gcd(3^n-2,2^n-3)=\gcd(5,2^n-3)$

Zagiers Class Number Definition of Binary Quadratic Forms

On odd perfect numbers and a GCD - Part V

Is there an Integral domain that is a GCD domain but NOT a UFD? [duplicate]

Show that any two consecutive odd integers are relatively prime

On odd perfect numbers and a GCD - Part VI

If $N = q^k n^2$ is an odd perfect number with special prime $q$, then can $N$ be of the form $q^k \cdot (\sigma(q^k)/2) \cdot {n}$?

Let $a\mid c$ and $b\mid c$ such that $\gcd(a,b)=1$, Show that $ab\mid c$