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2006 BAMO p2 2005, 2006 as sum of at least 2 consecutive odd pos. int.

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August 27, 2019
number theoryconsecutiveSumalgebra

Problem Statement

Since 24=3+5+7+924 = 3+5+7+9, the number 2424 can be written as the sum of at least two consecutive odd positive integers. (a) Can 20052005 be written as the sum of at least two consecutive odd positive integers? If yes, give an example of how it can be done. If no, provide a proof why not. (b) Can 20062006 be written as the sum of at least two consecutive odd positive integers? If yes, give an example of how it can be done. If no, provide a proof why not.