MathDB

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=2^{\alpha }3^{\beta }5^{\gamma }

(where

\alpha ,

\beta

and

\gamma

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.

Problem Statement