Proof of greatest common divisor
94770
Greatest common divisor of two positive integers
10348
Prove that if the $\gcd(a,b)=1$, then $\gcd(a+b,ab)=1$
43728
Proof via Group Theory : $\mathrm{lcm}(a,b) \cdot \gcd(a,b) = |ab|$
84417
Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$
52483
Showing that $(m)\cap (n)=(\operatorname{lcm}(m,n))$ and $(m)+(n)=(\gcd(m,n))$ for any $m,n\in\mathbb{Z}$
28021
Showing that these two definitions of $\gcd(a,b)$ are equivalent
128199
Proving gcd(a, a+2) is 1 or 2 for every integer a?
14693
$d = \gcd(c,m),\ ac≡bc\pmod{\! m}\Rightarrow a≡b\pmod {\!m/d}\ $ [Congruence Cancellation & Division Rule]
55441
Check: For the integers $a,b,c$ show that $\gcd(a,bc)=\gcd(a,\gcd(a,b)\cdot c)$
72747
Proving gcd($a,b$)lcm($a,b$) = $|ab|$
41295
Divisibility, LCM and GCD for fractions (rationals)
1713
number theory $\gcd(a,bc)=\gcd(a,c)$
6012
Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
107349
Working with elementary type proofs of divisor functions
67660
Prove $\,b\equiv c\pmod{\!m}\Rightarrow \gcd(b,m)=\gcd(c,m)$ i.e. $\gcd(c+km,m) = \gcd(c,m)$
43155
Cyclotomic Polynomials and GCD
77278
If $\,\gcd(a,b) = {\rm lcm}(a,b)\,$ then prove $a=b$