Question 132
Distinct real numbers $a, b, c$ satisfy the condition $a + \frac{1}{b} = b + \frac{1}{c} = c + \frac{1}{a}$. Find all possible values of the product $abc$:
1) for all real $a, b, c$;
2) for positive real $a, b, c$?
1) for all real $a, b, c$;
2) for positive real $a, b, c$?