Congruences and GCDs
21250
Prove $x \equiv a \pmod{p}$ and $x \equiv a \pmod{q}$ then $x \equiv a\pmod{pq}$
76507
$\gcd(b^x - 1, b^y - 1, b^ z- 1,\dots) = b^{\gcd(x, y, z,\dots)} -1$
38295
If $\gcd (a,b) = 1$, what can be said about $\gcd (a+b,a-b)$?
56803
Finding solutions to congruence equations
14693
$d = \gcd(c,m),\ ac≡bc\pmod{\! m}\Rightarrow a≡b\pmod {\!m/d}\ $ [Congruence Cancellation & Division Rule]
154959
Proof of associativity of GCD?
73391
Prove that if $\gcd(a,b)=1$, then $\gcd(a^2,b^2)=1$
66748
Show that if $a \equiv b \pmod n$, $\gcd(a,n)=\gcd(b,n)$
30045
Solving linear congruences by hand: modular fractions and inverses
142693
$\gcd(a,b) = \gcd(a + b, \mathrm{lcm}[a,b])$
34330
How to prove $\gcd(a^2,b^2) = (\gcd(a,b))^2$?
87013
If $\gcd(a,b)=1$, then there exists integers $x$ and $y$ such that $xa + yb = 1$
101872
Prove that $\gcd(a^2, b^2) = \gcd(a, b)^2$
37596
If $\gcd(a,b)= 1$ and $a$ divides $bc$ then $a$ divides $c\ $ [Euclid's Lemma]
2904
Solving linear congruence (modular inverse or fraction) via gcd Bezout equation
87846
If $\gcd (x,4) = 2$ and $\gcd(y,4) = 2$ then $\gcd(x+y,4) = 4$
33996
Proving that $\gcd(2^m - 1, 2^n - 1) = 2^{\gcd(m,n )} - 1$