MathDB
Sum over partitions

Source: 2024 Israel Olympic Revenge P2

June 20, 2024
olympic revengealgebra

Problem Statement

Let n≥2n\geq 2 be an integer. For each natural mm and each integer sequence 0<k1<k2<⋯<km0<k_1<k_2<\cdots <k_m for which k1+⋯+km=nk_1+\cdots+k_m=n, Michael wrote down the number 1k1⋅k2⋯km\frac{1}{k_1\cdot k_2\cdots k_m} on the board. Prove that the sum of the numbers on the board is less than 11.
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