AMO-Bench 2025 Problem 25
- Answer
Given a positive integer , find all positive integers that can be expressed in the form where .
Dataset text AMO-Bench. Open licence.
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The set S of all such positive integers n is given by: \begin{equation*} S= \begin{cases} {n | n=2 \text{ or } n-2 \text{ has an odd factor greater than 1}}, & \text{if } k=1,\ {n | n=2 \text{ or } n \geq 5}, & \text{if } k=2,\ {n | n=2 \text{ or } n \geq 4}, & \text{if } k=4,\ \mathbb{N}^{+}, & \text{if } k=3 \text{ or } k \geq 5. \end{cases} \end{equation*}
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