Find the minimum and maximum values of $ S=\frac{a}{b}+\frac{c}{d} $ where $a$, $b$, $c$, $d$ are positive integers satisfying $a + c = 20202$ and $b + d = 20200$.
Problem
Source: XIX OlimpĂada Matemática Rioplatense (2010)
Tags: inequalities, number theory unsolved, number theory