New posts in gcd-and-lcm

approximate greatest common divisor

algorithms gcd-and-lcm

Asymptotic behavior of number of triples $i,j,k\le n$ with pairwise bounded least common multiples each $\le n$.

number-theory asymptotics analytic-number-theory gcd-and-lcm upper-lower-bounds

Converse of Bézout's identity

elementary-number-theory gcd-and-lcm

gcd of power plus one

elementary-number-theory gcd-and-lcm

Finding a common factor of two coprime polynomials

abstract-algebra number-theory polynomials gcd-and-lcm

GCD of an empty set?

elementary-number-theory gcd-and-lcm

Prove that the order of the cyclic subgroup $\langle g^k\rangle $ is $n/{\operatorname{gcd}(n,k)}$ [duplicate]

abstract-algebra group-theory elementary-number-theory cyclic-groups gcd-and-lcm

prove that prime factorization allows to give you the gcd of two numbers [duplicate]

Find $\gcd(p^n-1,p^m+1)$.

elementary-number-theory prime-numbers divisibility gcd-and-lcm

How to show that $\displaystyle [a,b,c] = \frac{abc}{(ab,bc,ca)}$ without prime factorization?

elementary-number-theory least-common-multiple gcd-and-lcm

Showing $\gcd(n!i+1,n!j+1) = 1$ for $n \in \mathbb{N}$ if $i$ and $j$ are integers with $1\leq i < j \leq n$

elementary-number-theory divisibility factorial gcd-and-lcm

The difference of two coprime composites

elementary-number-theory modular-arithmetic arithmetic gcd-and-lcm conjectures

GCD of two whole complex numbers GCD(5-3i,7+i) in Z[i]

complex-numbers gcd-and-lcm

Can the identity $ab=\gcd(a,b)\text{lcm}(a,b)$ be recovered from this category?

elementary-number-theory category-theory divisibility gcd-and-lcm least-common-multiple

Find, with proof, all the integers $a$ that satisfy the equation $\gcd\left(a,\:10\right)\:=\:a.$ [duplicate]

divisibility gcd-and-lcm

Does the Bezout GCD equation hold in a UFD?

abstract-algebra ideals gcd-and-lcm

Can I make general formula for this problem

number-theory gcd-and-lcm

Why do we notate the greatest common divisor of $a$ and $b$ as $(a,b)$?

elementary-number-theory notation math-history gcd-and-lcm

Prove that either $m$ divides $n$ or $n$ divides $m$ given that $\operatorname{lcm}(m,n) + \operatorname{gcd}(m,n) = m + n$?

number-theory elementary-number-theory divisibility gcd-and-lcm

Let $a_1/b_1,\ldots,a_n/b_n$ be rational numbers in lowest terms. If $M={\rm lcm}(b_1,\ldots,b_n)$, prove $\gcd(Ma_1/b_1,\ldots,Ma_n/b_n)=1$.

number-theory elementary-number-theory gcd-and-lcm