Question 176
Find all positive integers $k$ for which the equation
$$
\operatorname{lcm}(m, n)-\gcd(m, n)=k(m-n)
$$
has no positive integer solutions $(m, n)$ with $m \neq n$.
$$
\operatorname{lcm}(m, n)-\gcd(m, n)=k(m-n)
$$
has no positive integer solutions $(m, n)$ with $m \neq n$.