Theory of Numbers Properties of GCD (Greatest Common Divisor)
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number theory $\gcd(a,bc)=\gcd(a,c)$
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If $\gcd(a,b)=1$, then $\gcd(a^n,b^n)=1$
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On the GCD of a Pair of Fermat Numbers
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Suppose the gcd (a,b) = 1 and c divides a + b. Prove that gcd (a,c) = 1 = gcd (b,c)
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$c\mid a,b\iff c\mid\gcd(a,b)$ [GCD Universal Property]
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GCD( LCM(a,b) , LCM(a,c) ) = LCM(b, GCD(b,c)) , why?
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How to prove that $z\gcd(a,b)=\gcd(za,zb)$
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Finding $\gcd(2n-1,2n+1)$ . . . I think it's 1 but is my logic right?
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If integers $a$ and $b$ are not both zero, then $\gcd(a,b)=\gcd(a-b,b)$
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Greatest common divisor of two positive integers
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I need some help with a GCD and LCM's Problem
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Prove that if d is a common divisor of a and b, then $d=\gcd(a,b)$ if and only if $\gcd(a/d,b/d)=1$
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$\gcd(b^x - 1, b^y - 1, b^ z- 1,\dots) = b^{\gcd(x, y, z,\dots)} -1$
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How to find GCD, LCM on a set of numbers
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Proving $\gcd((a+b)^m,(a-b)^m)\le2^m$ for coprime $a,b$ and $m \in \Bbb N$
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If $\gcd(a,b) = 1$ then $\gcd(a,a + b) = 1$
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Divisibility, LCM and GCD for fractions (rationals)