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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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possible solution | Comment 1 of 3

[1] 2n : n is a nonnegative integer
[2] There is no integer that cannot be written as the sum of two or more consecutive integers
[3] The number of ways a number can be represented is at least equal to (2n - 1) where n is the number of different odd prime factors in the number. Thus, only numbers with one odd prime factor may be written as the sum of 2 or more consecutive positive integers in one way.

Edited on April 15, 2011, 3:42 am
  Posted by Dej Mar on 2011-04-14 19:38:31

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