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.
by
Calvin Lin