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Spain Mathematical Olympiad 2007, Problem 4

Source: 2007 Spain Mathematical Olympiad

June 14, 2017
number theory

Problem Statement

What are the positive integer numbers that we are able to obtain in 20072007 distinct ways, when the sum is at least out of two positive consecutive integers? What is the smallest of all of them? Example: the number 9 is written in exactly two such distinct ways: 9=4+59 = 4 + 5 9=2+3+4.9 = 2 + 3 + 4.
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