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MathNet 2016-part-06 — 184 problems (EN–VI) Question 144

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

Question 144

Numbers $a$, $b$, $c$ satisfy the conditions:
$$
a^2 + 2 = b^4, \quad b^2 + 2 = c^4, \quad c^2 + 2 = a^4.
$$
What values can take expression
$(a^2 - 1)(b^2 - 1)(c^2 - 1)$?