If gcd(a,b)=1 and c|(a+b), then gcd(a,c)=gcd(b,c)=1

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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
If gcd(a,b)=1, then gcd(ac,b)=gcd(c,b) If gcd(a,b)=1, then gcd(ac,b)=gcd(c,b)
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 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.
If gcd(a,b)=1, d|ac, and d|bc, then d|c. If gcd(a,b)=1, d|ac, and d|bc, then d|c.
If c|a and c|b, then c|gcd(a, b) If c|a and c|b, then c|gcd(a, b)
Prove gcd(a,bc) = 1 if and only if gcd(a,b) = 1 and gcd(a,c) = 1 (ILIEKMATHPHYSICS) Prove gcd(a,bc) = 1 if and only if gcd(a,b) = 1 and gcd(a,c) = 1 (ILIEKMATHPHYSICS)
Show that if gcd(a,b)=1 and gcd(a,c)=1, then gcd(a, bc)=1 [NT-Ch.2-S2.5] - Part 9 Show that if gcd(a,b)=1 and gcd(a,c)=1, then gcd(a, bc)=1 [NT-Ch.2-S2.5] - Part 9