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Romania TST 2016 Day 1 P3

Source: Romania TST 2016 Day 1 P3

November 1, 2017
number theorynumber divisors

Problem Statement

Let nn be a positive integer, and let a1,a2,..,ana_1,a_2,..,a_n be pairwise distinct positive integers. Show that ∑k=1n1[a1,a2,…,ak]<4,\sum_{k=1}^{n}{\frac{1}{[a_1,a_2,…,a_k]}} <4, where [a1,a2,…,ak][a_1,a_2,…,a_k] is the least common multiple of the integers a1,a2,…,aka_1,a_2,…,a_k.
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