Elementary Number Theory GCD
422
If $\gcd(a,b)=1$, $\gcd(a,y)=1$ and $\gcd(b,x)=1$ then prove that $ax+by$ is prime to $ab$
76507
$\gcd(b^x - 1, b^y - 1, b^ z- 1,\dots) = b^{\gcd(x, y, z,\dots)} -1$
34738
Prove that $\gcd(n!+1,(n+1)!+1)=1$
157784
Prove that if $\gcd(ab,c)=1$, then $\gcd(a,c)=1$.
23066
If $\gcd(a, b) = 1$, then $\gcd(ab, c) = \gcd(a, c) \cdot\gcd(b, c)$
73391
Prove that if $\gcd(a,b)=1$, then $\gcd(a^2,b^2)=1$
74809
GCD to LCM of multiple numbers
10966
gcd and lcm from prime factorization proof
117098
Properties of the greatest common divisor: $\gcd(a, b) = \gcd(a, b-a)$ and $\gcd(a, b) = \gcd(a, b \text{ mod } a)$
56423
gcd of power plus one
7091
If $\gcd(a,b)=1$, then $\gcd(a^n,b^n)=1$
51858
Showing $\gcd(2^m-1,2^n+1)=1$
4425
Why are integer GCDs positive? [unit normalization of GCDs]
65687
$\gcd(a,b)\gcd(x,y)\mid ax+by$
10348
Prove that if the $\gcd(a,b)=1$, then $\gcd(a+b,ab)=1$
82777
If $\gcd(a, b) = 1$ then prove that $\gcd(a+b, a^2-ab+b^2) = 1$ or $3$?
37808
Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$