4 papers
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…
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{…
A Proof of Ramanujan's Classic Formula
Thang Pang Ern, Devandhira Wijaya Wangsa
In 1914, Ramanujan presented a collection of 17 elegant and rapidly converging formulae for . Among these, one of the most celebrated is the following series: \[\frac{1}Ï=\fra…
Finding Squares in a Product of Squares
Thang Pang Ern
We wish to discuss positive integer solutions to the Diophantine equation Some methods in analytic number theory will be used to tackle this problem.