New posts in gcd-and-lcm

Prove $\, a_1 \Bbb Z \cap \dotsb \cap a_r \mathbb{Z} = {\rm lcm}(a_1, \ldots, a_r) \Bbb Z\ $ [lcm = ideal intersection]

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

$\gcd\left(a+b,\frac{a^p+b^p}{a+b}\right)=1$, or $p$

elementary-number-theory divisibility gcd-and-lcm

How to calculate GCD of Gaussian integers? [closed]

abstract-algebra number-theory ring-theory complex-numbers gcd-and-lcm

Find $x,y$ given $\gcd(x,y)$ and ${\rm lcm}(x,y)$

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

If $\gcd(a, b) = 1$, then $\gcd(ab, c) = \gcd(a, c) \cdot\gcd(b, c)$

elementary-number-theory divisibility gcd-and-lcm

If $\gcd(a,b)=1$, then $\gcd(a+b,a^2 -ab+b^2)=1$ or $3$.

elementary-number-theory divisibility gcd-and-lcm

Prove that any two consecutive terms of the Fibonacci sequence are relatively prime

elementary-number-theory solution-verification gcd-and-lcm fibonacci-numbers

Why is $\gcd(x^4+1,x^2-1) = 1$ but I get $2$? [unit normalization of gcds]

polynomials divisibility gcd-and-lcm

GCD to LCM of multiple numbers

elementary-number-theory gcd-and-lcm

Integral domain with two elements that do not have a gcd

abstract-algebra gcd-and-lcm

How to use fundamental theorem of arithmetic to conclude that $\gcd(a^k,b^n)=1$ for all $k, n \in$ N whenever $a,b \in$ N with $\gcd(a,b)=1$?

number-theory elementary-number-theory arithmetic gcd-and-lcm prime-factorization

Why are integer GCDs positive? [unit normalization of GCDs]

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

Divisor of a product of integers is a product of divisors

elementary-number-theory divisibility gcd-and-lcm

Greatest common divisor is the smallest positive number that can be written as $sa+tb$

elementary-number-theory divisibility gcd-and-lcm

For integers $a$ and $b$, $ab=\text{lcm}(a,b)\cdot\text{hcf}(a,b)$

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

GCD Proof with Multiplication: gcd(ax,bx) = x$\cdot$gcd(a,b)

elementary-number-theory divisibility gcd-and-lcm

If $(a,b)=1$ then prove $(a+b, ab)=1$.

elementary-number-theory gcd-and-lcm coprime

Concise proof that every common divisor divides GCD without Bezout's identity?

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

$b \mid ac\Rightarrow b \mid (a,b)(c,b)\,$ for integers $\,a,b,c$

elementary-number-theory divisibility gcd-and-lcm

$\gcd(a,\operatorname{lcm}(b,c))=\operatorname{lcm}(\gcd(a,b),\gcd(a,c))$

elementary-number-theory gcd-and-lcm