The Answer Is At Least 1

Number Theory Level 3

How many positive integers $m$ are there, such that for some triple of positive integers $(a, b, c)$ , we have

$m = \frac{ a}{b} + \frac{b}{c} + \frac{c}{a}?$

For example, if $a = b = c$ , then we get the value $\frac{1}{1} + \frac{1}{1} + \frac{1}{1} = 3$ .

Hence, the answer is "at least 1", which applies to all 4 options. You need to figure out which is correct.