On the Limiting Density of a gcd Map

Thang Pang Ern, Malcolm Tan Jun Xi, Loh Wei Xuan Ryan

The function \[f(a,b)=\frac{\gcd(a+b,ab)}{\gcd(a,b)}\] is of interest in this paper. We then ask a natural question regarding how often $f(a,b)=1$ is. We yield the limiting density…