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MathNet 2024-part-04 — 168 problems (EN–VI) Question 105

Math Olympiad Vault · MathNet 2024-part-04 — 168 problems (EN–VI)

Question 105

A natural number $n \ge 2$ is called *special* if there exist $n$ odd natural numbers whose sum is equal to their product.

a) Prove that $5$ is a special number.

b) Determine how many special numbers are in the set $\{2, 3, \dots, 2024\}$.