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MathNet 2008-part-03 — 165 problems (EN–VI) Question 63

Math Olympiad Vault · MathNet 2008-part-03 — 165 problems (EN–VI)

Question 63

Find all triples of positive integers $(x, y, z)$ such that
$$
xyz + xy + yz + zx + x + y + z = 243.
$$