IMO Shortlist 1990 problem 1


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2. travnja 2012.
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The integer 9 can be written as a sum of two consecutive integers: 9 = 4+5. Moreover, it can be written as a sum of (more than one) consecutive positive integers in exactly two ways: 9 = 4+5 = 2+3+4. Is there an integer that can be written as a sum of 1990 consecutive integers and that can be written as a sum of (more than one) consecutive positive integers in exactly 1990 ways?
Izvor: Međunarodna matematička olimpijada, shortlist 1990