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6

Part of 1985 Czech And Slovak Olympiad IIIA

Problems(1)

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

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

9/11/2024
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.
number theorydivides