IMO Shortlist 1990 problem 1
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The integer
can be written as a sum of two consecutive integers:
Moreover, it can be written as a sum of (more than one) consecutive positive integers in exactly two ways:
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?





Izvor: Međunarodna matematička olimpijada, shortlist 1990