Prove gcd(a,b) = gcd(a+c,b) given b|c
190
Why $\gcd(qb+r,b)=\gcd(b,r)$?
82777
If $\gcd(a, b) = 1$ then prove that $\gcd(a+b, a^2-ab+b^2) = 1$ or $3$?
33996
Proving that $\gcd(2^m - 1, 2^n - 1) = 2^{\gcd(m,n )} - 1$
10348
Prove that if the $\gcd(a,b)=1$, then $\gcd(a+b,ab)=1$
84417
Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$
2208
$\gcd(a,b,c)=\gcd(\gcd(a,b),c)\,$ [GCD Associative Law]
15168
If $a,b$ are positive integers such that $\gcd(a,b)=1$, then show that $\gcd(a+b, a-b)=1$ or $2$. and $\gcd(a^2+b^2, a^2-b^2)=1$ or $2 $
23066
If $\gcd(a, b) = 1$, then $\gcd(ab, c) = \gcd(a, c) \cdot\gcd(b, c)$
31465
Prove that if $a \mid b$ then $\gcd(a,b) = |a|$
66748
Show that if $a \equiv b \pmod n$, $\gcd(a,n)=\gcd(b,n)$
105832
prove that if $\gcd(a,b)=1$ then $\gcd(a^2, b^2)=1$
65687
$\gcd(a,b)\gcd(x,y)\mid ax+by$
36
Prove: If $\gcd(a,b,c)=1$ then there exists $z$ such that $\gcd(az+b,c) = 1$
52546
How can I find the possible values that $\gcd(a+b,a^2+b^2)$ can take, if $\gcd(a,b)=1$
128199
Proving gcd(a, a+2) is 1 or 2 for every integer a?
77278
If $\,\gcd(a,b) = {\rm lcm}(a,b)\,$ then prove $a=b$
147527
Let $a$ and $b$ be non-zero integers, and $c$ be an integer. Let $d = \gcd(a, b)$. Prove that if $a|c$ and $b|c$ then $ab|cd$.