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Natural sequences with summation condition

Source: Spain National Olympiad 2009 (OME), Problem 1

January 2, 2010
number theory proposednumber theory

Problem Statement

Find all the finite sequences with n n consecutive natural numbers a1,a2,...,an a_1, a_2,..., a_n, with n≥3 n\geq3 such that a_1\plus{} a_2\plus{}...\plus{} a_n\equal{}2009.
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