Consecutive sums
a) Which positive integers can be written as a sum of consecutive positive integers? For example, 21 can be written
as 6+7+8, 5 can be written as 2+3, and 88 can be written as 3+4+5+6+7+8+9+10+11+12+13. Try to justify your
result.
b) Some positive integers can be written as a sum of consecutive positive integers in more than one way. For
example, 15 can be written as 1+2+3+4+5 or 4+5+6 or 7+8. Try to find an algorithm for finding all of the ways a
given positive integer N can be written as a sum of consecutive integers (i.e., if a particular N walks up to you on the
street, you should be able to apply your algorithm to it and produce all sums of consecutive integers equal to that N).
Let’s get a start:
1
20
2
21
3
22
4
23
5
24
6
25
7
26
8
27
9
28
10
29
11
30
12
31
13
32
14
33
15
34
16
35
17
36
18
37
19
38