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MathNet 2016-part-06 — 184 problems (EN–VI) Question 148

Math Olympiad Vault · MathNet 2016-part-06 — 184 problems (EN–VI)

Question 148

Numbers $a$, $b$, $c$ satisfy the conditions:
$$
\frac{a+c}{a+1} = b, \quad \frac{c+b}{c+1} = a, \quad \frac{b+a}{b+1} = c.
$$

What values can the expression $(a+1)(b+1)(c+1)$ take?