A given natural number N is being decomposed in a sum of some consecutive integers.
a.) Find all such decompositions for N=500.
b.) How many such decompositions does the number N=2α3β5γ (where α, β and γ are natural numbers) have? Which of these decompositions contain natural summands only?
c.) Determine the number of such decompositions (= decompositions in a sum of consecutive integers; these integers are not necessarily natural) for an arbitrary natural N.
Note by Darij: The 0 is not considered as a natural number. number theorySummationequationIMO ShortlistIMO Longlist