MathDB
Cute counting

Source: KMO 2022 P4

October 29, 2022
inequalitiescombinatorics

Problem Statement

For positive integers m,nm, n (m>nm>n), an+1,an+2,...,ama_{n+1}, a_{n+2}, ..., a_m are non-negative integers that satisfy the following inequality. 2>an+1n+1≥an+2n+2≥⋯≥amm 2> \frac{a_{n+1}}{n+1} \ge \frac{a_{n+2}}{n+2} \ge \cdots \ge \frac{a_m}{m} Find the number of pair (an+1,an+2,⋯ ,am)(a_{n+1}, a_{n+2}, \cdots, a_m).
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