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math.NT2026
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 is. We yield the limiting density…
math.NT2026
On the Asymptotic Density of a GCD-based Map
Thang Pang Ern, Malcolm Tan Jun Xi
We show that the symmetry of \[f\left(a,b\right)=\frac{\operatorname{gcd}\left(ab,a+b\right)}{\operatorname{gcd}\left(a,b\right)}\] stems from an $\operatorname{SL}_2\left(\mathbb{…