Question 35
Prove that the equation
$$
\frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{1}{abc} = \frac{12}{a + b + c}
$$
has many solutions $(a, b, c)$ in strictly positive integers.
$$
\frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{1}{abc} = \frac{12}{a + b + c}
$$
has many solutions $(a, b, c)$ in strictly positive integers.