Newbetuts

Prove that $n!=\prod_{k=1}^n \operatorname{lcm}(1,2,...,\lfloor n/k \rfloor)$ for any $n \in \mathbb N$

Are there arbitrarily large sets $S$ of natural integers such that the difference of each pair is their GCD?

Prove that $\gcd(a^2, b^2) = \gcd(a, b)^2$ [duplicate]

Hint for $(n!+1,(n+1)!)$, stuck at $ (n!+1,n+1)$

If GCD $(a_1,\ldots, a_n)=1$ then there's a matrix in $SL_n(\mathbb{Z})$ with first row $(a_1,\ldots, a_n)$

Relation between $\gcd$ and Euler's totient function .

Prove that a cyclic group with only one generator can have at most 2 elements

GCD in arbitrary domain

Bezout's identity in $F[x]$

If $x;y$ $\in T$($x$ and $y$ can be the same), then $x^2-y \in T $ Prove that : $T = \mathbb Z $

Showing $\gcd(n^3 + 1, n^2 + 2) = 1$, $3$, or $9$

A condition for being a prime: $\;\forall m,n\in\mathbb Z^+\!:\,p=m+n\implies \gcd(m,n)=1$

If $\gcd(a, b) = 1$ then prove that $\gcd(a+b, a^2-ab+b^2) = 1$ or $3$? [duplicate]

In an Integral Domain is it true that $\gcd(ac,ab) = a\gcd(c,b)$?

Let $a,k,m$ be integers. Prove that $\gcd(ka,km) = k\gcd(a,m)$.

Show that $\gcd(a,bc)=1$ if and only if $\gcd(a,b)=1$ and $\gcd(a,c)=1$

New posts in gcd-and-lcm

Prove that $n!=\prod_{k=1}^n \operatorname{lcm}(1,2,...,\lfloor n/k \rfloor)$ for any $n \in \mathbb N$

How to prove gcd of consecutive Fibonacci numbers is 1? [duplicate]

Compute gcd of values of a quadratic polynomial

Failure of existence of GCD

Prove that if the $\gcd(a,b)=1$, then $\gcd(a+b,ab)=1$ [duplicate]

Are there arbitrarily large sets $S$ of natural integers such that the difference of each pair is their GCD?

Prove that $\gcd(a^2, b^2) = \gcd(a, b)^2$ [duplicate]

Hint for $(n!+1,(n+1)!)$, stuck at $ (n!+1,n+1)$

If GCD $(a_1,\ldots, a_n)=1$ then there's a matrix in $SL_n(\mathbb{Z})$ with first row $(a_1,\ldots, a_n)$

Relation between $\gcd$ and Euler's totient function .

Prove that a cyclic group with only one generator can have at most 2 elements

GCD in arbitrary domain

Bezout's identity in $F[x]$

If $x;y$ $\in T$($x$ and $y$ can be the same), then $x^2-y \in T $ Prove that : $T = \mathbb Z $

Showing $\gcd(n^3 + 1, n^2 + 2) = 1$, $3$, or $9$

A condition for being a prime: $\;\forall m,n\in\mathbb Z^+\!:\,p=m+n\implies \gcd(m,n)=1$

If $\gcd(a, b) = 1$ then prove that $\gcd(a+b, a^2-ab+b^2) = 1$ or $3$? [duplicate]

In an Integral Domain is it true that $\gcd(ac,ab) = a\gcd(c,b)$?

Let $a,k,m$ be integers. Prove that $\gcd(ka,km) = k\gcd(a,m)$.

Show that $\gcd(a,bc)=1$ if and only if $\gcd(a,b)=1$ and $\gcd(a,c)=1$