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a_{k+1} divides a_1+a_2+...+a_k

Source: Czech and Slovak Olympiad 1985, National Round, Problem 6

September 11, 2024
number theorydivides

Problem Statement

Prove that for every natural number n>1n > 1 there exists a suquence a1a_1,a2a_2, ......, ana_n of the numbers 1,2,...,n1,2,...,n such that for each k∈{1,2,...,n−1}k \in \{1,2,...,n-1\} the number ak+1a_{k+1} divides a1+a2+...+aka_1+a_2+...+a_k.
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