Question 37
A natural number $n$ is interesting if it can be written as $n = \lfloor \frac{1}{a} \rfloor + \lfloor \frac{1}{b} \rfloor + \lfloor \frac{1}{c} \rfloor$, where $a, b$ and $c$ are positive real numbers, such that $a + b + c = 1$.
Determine all the interesting numbers. ($[x]$ denotes the floor of the real number $x$.)
Determine all the interesting numbers. ($[x]$ denotes the floor of the real number $x$.)