Problem of the Month for October, 2005

Problem:

The number 42 can be written as the sum of consecutive integers in a number of different ways. For example, here are two such ways (there are more besides these):

42 = 13+14+15 and
42 = (-12)+(-11)+...+( -1)+0+1+...+13+14+15.

In how many different ways can the number 105 be written as a sum of consecutive integers? Say how many ways there are, write down each of these ways, and then explain why there are no others ways.

Possible generalizations you might consider:

Describe a general algorithm that could used for finding different ways of writing an arbitrary integer n as the sum of consecutive integers.

Answer:

You will need Adobe Acrobat Reader to read this answer since it is stored in PDF format.
PDF