Prove gcd(a,bc) = 1 if and only if gcd(a,b) = 1 and gcd(a,c) = 1 (ILIEKMATHPHYSICS)

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Prove in a group, if gcd(|a|,|b|) = 1, then ⟨a⟩ ∩ ⟨b⟩ = {e} (ILIEKMATHPHYSICS) Prove in a group, if gcd(|a|,|b|) = 1, then ⟨a⟩ ∩ ⟨b⟩ = {e} (ILIEKMATHPHYSICS)
If gcd(a,b)=1 and c|a, then gcd(b,c)=1 If gcd(a,b)=1 and c|a, then gcd(b,c)=1
Prove if gcd(a,b) = 1 then gcd(a^n,b^n) = 1 [ILIEKMATHPHYSICS] Prove if gcd(a,b) = 1 then gcd(a^n,b^n) = 1 [ILIEKMATHPHYSICS]
If gcd(a,b)=1 and gcd(a,c)=1, then gcd(a,bc)=1. If gcd(a,b)=1 and gcd(a,c)=1, then gcd(a,bc)=1.
Bewijs: Als ggd(𝑎, 𝑚) = 1 en ggd(𝑏, 𝑚) = 1, dan is ggd(𝑎𝑏, 𝑚) = 1 | Getallentheorie | Abstracte a... Bewijs: Als ggd(𝑎, 𝑚) = 1 en ggd(𝑏, 𝑚) = 1, dan is ggd(𝑎𝑏, 𝑚) = 1 | Getallentheorie | Abstracte a...
If gcd(a,b)=1 and c|(a+b), then gcd(a,c)=gcd(b,c)=1 If gcd(a,b)=1 and c|(a+b), then gcd(a,c)=gcd(b,c)=1
If a|b+c and gcd(b,c)=1, then gcd(a,b)=1=gcd(a,c). If a|b+c and gcd(b,c)=1, then gcd(a,b)=1=gcd(a,c).
If gcd(a,b)=1, then gcd(ac,b)=gcd(c,b) If gcd(a,b)=1, then gcd(ac,b)=gcd(c,b)