Question 17
For positive real numbers $a,b,c$, find the minimum value of $u=\left\lfloor\dfrac{a+b}{c}\right\rfloor+\left\lfloor\dfrac{b+c}{a}\right\rfloor+\left\lfloor\dfrac{c+a}{b}\right\rfloor$. Here $\lfloor t\rfloor$ denotes the greatest integer not exceeding $t$.