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New posts in gcd-and-lcm
Motivation behind the definition of GCD and LCM
abstract-algebra
elementary-number-theory
gcd-and-lcm
unique-factorization-domains
motivation
Show that $\gcd\left(\frac{a^n-b^n}{a-b},a-b\right)=\gcd(n d^{n-1},a-b)$
number-theory
elementary-number-theory
divisibility
gcd-and-lcm
Comaximal ideals in a commutative ring
abstract-algebra
commutative-algebra
ideals
gcd-and-lcm
Fibonacci divisibilty properties $ F_n\mid F_{kn},\,$ $\, \gcd(F_n,F_m) = F_{\gcd(n,m)}$
elementary-number-theory
modular-arithmetic
divisibility
fibonacci-numbers
gcd-and-lcm
Prove: If $\gcd(a,b,c)=1$ then there exists $z$ such that $\gcd(az+b,c) = 1$
abstract-algebra
elementary-number-theory
divisibility
gcd-and-lcm
$ d_1,d_2\mid n\iff {\rm lcm}(d_1,d_2)\mid n\ $ [LCM Universal Property]
elementary-number-theory
gcd-and-lcm
If $a \mid m$ and $(a + 1) \mid m$, prove $a(a + 1) | m$.
number-theory
divisibility
gcd-and-lcm
least-common-multiple
Show $GCD(a_1, a_2, a_3, \ldots , a_n)$ is the least positive integer that can be expressed in the form $a_1x_1+a_2x_2+ \ldots +a_nx_n$
elementary-number-theory
gcd-and-lcm
$\gcd(a,b,c)=\gcd(\gcd(a,b),c)\,$ [Associative Law for GCD, LCM]
elementary-number-theory
divisibility
gcd-and-lcm
Prove that $(ma, mb) = |m|(a, b)\ $ [GCD & LCM Distributive Law]
elementary-number-theory
divisibility
gcd-and-lcm
Why $\gcd(b,qb+r)=\gcd(b,r),\,$ so $\,\gcd(b,a) = \gcd(b,a\bmod b)$
abstract-algebra
elementary-number-theory
divisibility
gcd-and-lcm
How to use the Extended Euclidean Algorithm manually?
elementary-number-theory
algorithms
gcd-and-lcm
euclidean-algorithm
Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
elementary-number-theory
induction
divisibility
gcd-and-lcm
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