New posts in gcd-and-lcm

Pairs of numbers with a given LCM

combinatorics number-theory gcd-and-lcm

Why are Fibonacci numbers bad for Euclid's Algorithm and how to derive this upper bound on number of steps needed in general?

elementary-number-theory fibonacci-numbers gcd-and-lcm euclidean-algorithm

Proving that $\gcd\left(\frac a {\gcd(a,b)},\frac b {\gcd(a,b)}\right) =1$

elementary-number-theory gcd-and-lcm

For natural numbers $a$ and $b$, show that $a \Bbb Z + b \Bbb Z = \gcd(a, b)\Bbb Z $ [duplicate]

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

Prove that if $a$ and $b$ are relatively prime, then $\gcd(a+b, a-b) = 1$ or $2$ [duplicate]

elementary-number-theory divisibility gcd-and-lcm

Looking for an example of a GCD domain which is not a UFD

commutative-algebra divisibility integral-domain unique-factorization-domains gcd-and-lcm

Proof of Bezout's Lemma using Euclid's Algorithm backwards

elementary-number-theory proof-writing gcd-and-lcm

n-ary version of gcd$(a,b)\space $lcm$(a,b)$ = $ab$

number-theory gcd-and-lcm

Any least common multiple is larger than n, then the sum of inverse is bounded

elementary-number-theory gcd-and-lcm

The Chinese remainder theorem and distributive lattices

ring-theory gcd-and-lcm lattice-orders

Show that if $\gcd(a,3)=1$ then $a^7 \equiv a\pmod{63}$. Why is this assumption necessary?

discrete-mathematics modular-arithmetic gcd-and-lcm

Show that if $ar + bs = 1$ for some $r$ and $s$ then $a$ and $b$ are relatively prime

elementary-number-theory divisibility gcd-and-lcm

In a UFD, lcm = product for coprimes: $\,(a,b)=1,\ a,b\mid c\Rightarrow ab\mid c$

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

Given an integer $a$, suppose $d=\gcd(3a+5,\,5a+7)>2$. Determine $d$.

gcd-and-lcm

For $D$ a GCD domain , let $a,b,x \in D \setminus \{0\}$ , then is it true that $\gcd (ax,bx)=x \cdot \gcd (a,b)$? [duplicate]

ring-theory gcd-and-lcm integral-domain

If $\gcd (a,b) = 1$, what can be said about $\gcd (a+b,a-b)$? [duplicate]

elementary-number-theory divisibility gcd-and-lcm

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

elementary-number-theory gcd-and-lcm

Prove the LCM (Least Common Multiple).

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

If $n,m \in \mathbb{N}$ then there are $c,d$ such that $cd = (m,n)$, $(c,d) = 1$ and $(m/c,n/d) = 1$.

elementary-number-theory gcd-and-lcm

Is greatest common divisor of two numbers really their smallest linear combination?

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