A integer can be written as the sum of 1990 integers
Source: IMO ShortList 1990, Problem 1 (AUS 3)
November 2, 2005
number theoryAdditive combinatoricsAdditive Number TheorycountingIMO Shortlist
Problem Statement
The integer can be written as a sum of two consecutive integers: 9 \equal{} 4\plus{}5. Moreover, it can be written as a sum of (more than one) consecutive positive integers in exactly two ways: 9 \equal{} 4\plus{}5 \equal{} 2\plus{}3\plus{}4. Is there an integer that can be written as a sum of consecutive integers and that can be written as a sum of (more than one) consecutive positive integers in exactly ways?