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Only a finite number of integers cannot be represented

Source: Chinese MO 2004

September 25, 2011

inductionnumber theory proposednumber theory

Problem Statement

Prove that every positive integer

n

, except a finite number of them, can be represented as a sum of

2004

positive integers:

n=a_1+a_2+\cdots +a_{2004}

, where

1\le a_1<a_2<\cdots <a_{2004}

, and

a_i \mid a_{i+1}

for all

1\le i\le 2003

.
Chen Yonggao