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MathNet 2019-part-03 — 184 problems (EN–VI) Question 183

Math Olympiad Vault · MathNet 2019-part-03 — 184 problems (EN–VI)

Question 183

Find all the triplets $(x, y, z)$ of positive integers satisfying the following conditions:
$$
x + xy + xyz = 31, \quad x \lt y \lt z.
$$