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Unconsecutive-summables (Posted on 2011-04-14) Difficulty: 3 of 5
[1] Find all positive integers that cannot be written as the sum of 2 or more consecutive positive integers.

[2] Find all integers that cannot be written as the sum of 2 or more consecutive integers.

[3] Find all positive integers that can only be written as the sum of 2 or more consecutive positive integers in one way.

See The Solution Submitted by Jer    
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Some Thoughts Part 2 (spoiler) | Comment 2 of 3 |
There are no integers that cannot be written as the sum of two or more consecutive integers.

If n is positive, it equals the sum of all the 2n integers
     between -n+1 and n (inclusive)

If n is negative,
    it equals the sum of all the -2n integers between n and -n-1 (inclusive)

if n is zero, it is the sum of -1, 0 and 1.


Edited on April 14, 2011, 8:28 pm

Edited on April 14, 2011, 8:29 pm
  Posted by Steve Herman on 2011-04-14 20:27:20

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