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

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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
||Lecture#15||If a|c and b|c with gcd(a,b)=1 then ab|c||Prof.Latif Sajid||Number Theory|| ||Lecture#15||If a|c and b|c with gcd(a,b)=1 then ab|c||Prof.Latif Sajid||Number Theory||
||Lecture#19||If gcd(a,b)=1 then gcd(ac,b)=gcd(c,b)||Number Theory||Prof.Latif Sajid ||Lecture#19||If gcd(a,b)=1 then gcd(ac,b)=gcd(c,b)||Number Theory||Prof.Latif Sajid
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 c|a and c|b, then c|gcd(a, b) If c|a and c|b, then c|gcd(a, b)
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 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 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.