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New posts in gcd-and-lcm
$\gcd(b^x - 1, b^y - 1, b^ z- 1,\dots) = b^{\gcd(x, y, z,\dots)} -1$ [duplicate]
elementary-number-theory
divisibility
gcd-and-lcm
perfect-powers
Prove: If $a\mid m$ and $b\mid m$ and $\gcd(a,b)=1$ then $ab\mid m$
elementary-number-theory
divisibility
gcd-and-lcm
Proving that if $ad-bc = \pm 1$, then $\gcd(x,y) = \gcd(ax +by, cx + dy)$
elementary-number-theory
gcd-and-lcm
Proving $\gcd \left(\frac{a}{\gcd (a,b)},\frac{b}{\gcd (a,b)}\right)=1$
elementary-number-theory
proof-writing
divisibility
gcd-and-lcm
prove that $\operatorname{lcm}(n,m) = nm/\gcd(n,m)$
elementary-number-theory
divisibility
gcd-and-lcm
least-common-multiple
Proof of $\gcd(a,b)=ax+by\ $ [Bezout's identity]
abstract-algebra
elementary-number-theory
proof-writing
divisibility
gcd-and-lcm
$c\mid a,b\iff c\mid\gcd(a,b)$ [GCD Universal Property]
elementary-number-theory
divisibility
gcd-and-lcm
If $\gcd(a,b)= 1$ and $a$ divides $bc$ then $a$ divides $c\ $ [Euclid's Lemma]
elementary-number-theory
divisibility
solution-verification
gcd-and-lcm
If $\gcd(a,b)=1$, then $\gcd(a^n,b^n)=1$
elementary-number-theory
divisibility
gcd-and-lcm
Justifying expansion: $\gcd(a,c) \cdot \gcd(b,c) = \gcd(ab,bc,ac,cc)$
elementary-number-theory
gcd-and-lcm
When does the modular law apply to ideals in a commutative ring
abstract-algebra
commutative-algebra
gcd-and-lcm
What is $\gcd(0,0)$?
elementary-number-theory
discrete-mathematics
divisibility
gcd-and-lcm
How to prove $\,x^a-1 \mid x^b-1 \iff a\mid b$
elementary-number-theory
divisibility
gcd-and-lcm
How to show $a,b$ coprime to $n\Rightarrow ab$ coprime to $n$?
elementary-number-theory
gcd-and-lcm
Proof that $\gcd(ax+by,cx+dy)=\gcd(x,y)$ if $ad-bc= \pm 1$
elementary-number-theory
gcd-and-lcm
How to prove that $z\gcd(a,b)=\gcd(za,zb)$
abstract-algebra
elementary-number-theory
divisibility
gcd-and-lcm
Prove that if $\gcd( a, b ) = 1$ then $\gcd( ac, b ) = \gcd( c, b ) $
elementary-number-theory
gcd-and-lcm
Order of elements is lcm-closed in abelian groups
group-theory
elementary-number-theory
gcd-and-lcm
$\gcd(a,b)\!=\!1\!=\!\gcd(a,c)\Rightarrow\gcd(a,bc)\!=\!1$ [coprimes to $\,a\,$ are product closed]
elementary-number-theory
divisibility
gcd-and-lcm
Prove $\gcd(a+b, a-b) = 1$ or $2\,$ if $\,\gcd(a,b) = 1$
elementary-number-theory
divisibility
gcd-and-lcm
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