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sum of all products of k_1k_2...k_{999} (VI Soros Olympiad 1990-00 R3 11.2)

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May 28, 2024
algebranumber theory

Problem Statement

Find the sum of all possible products of natural numbers of the form k1k2...k999k_1k_2...k_{999}, where in each product k1<k2<...<k999<1999 k_1 < k_2 < ... < k_{999} <1999, and there are no kik_i and kjk_j such that ki+kj=1999k_i + k_j =1999.
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