Positive integers $a,b,c,d$ satisfy $a+c=10$ and \[\displaystyle S=\frac{a}{b} + \frac{c}{d} <1.\] Find the maximum value of $S$.
Problem
Source: Taiwan 2nd TST 2005, final exam, second day, problem 4
Tags: number theory unsolved, number theory
Source: Taiwan 2nd TST 2005, final exam, second day, problem 4
Tags: number theory unsolved, number theory
Positive integers $a,b,c,d$ satisfy $a+c=10$ and \[\displaystyle S=\frac{a}{b} + \frac{c}{d} <1.\] Find the maximum value of $S$.