Question #1527

Let a, b be nonzero integers. Show that gcd(a,b)=1 if and only if gcd(a+b,ab)=1.

Expert's answer

If gcd(a+b,ab)=p, p>1. Then if p |a from here p | a+b and p | b,

so gcd(a,b)=p but gcd(a,b)=1.

contradiction

Similarly to the other side.

so gcd(a,b)=p but gcd(a,b)=1.

contradiction

Similarly to the other side.

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