# consecutive numbers

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• Jul 6th 2006, 01:05 PM
Judi
consecutive numbers
which of the following cannot be expressed as the sum of two or more consecutive positive integers?
a. 17 b. 22 c. 24 d. 26 e. 32
• Jul 6th 2006, 01:42 PM
Quick
Quote:

Originally Posted by Judi
which of the following cannot be expressed as the sum of two or more consecutive positive integers?
a. 17 b. 22 c. 24 d. 26 e. 32

a. 8+9=17
b. 4+5+6+7=22
c. 7+8+9=24
d. 5+6+7+8=26

and nothing equals 32 (if you want to know my method of doing this, feel free to ask)
• Jul 6th 2006, 01:51 PM
ThePerfectHacker
Quote:

Originally Posted by Judi
which of the following cannot be expressed as the sum of two or more consecutive positive integers?
a. 17 b. 22 c. 24 d. 26 e. 32

A longgg time ago this question was discussed here on the forums. Click here to get BsOd

According to the thread those are the numbers that are powers of two. Thus, 32 is the answer cuz,
$32=2^5$
• Jul 6th 2006, 01:59 PM
Judi
Thank you,
Judi
• Jul 6th 2006, 02:02 PM
Quick
Quote:

Originally Posted by ThePerfectHacker
A longgg time ago this question was discussed here on the forums. Click here to get BsOd

According to the thread those are the numbers that are powers of two. Thus, 32 is the answer cuz,
$32=2^5$

I haven't come up with a proof for it, I just used logic, but I found that if a number is not divisible by any odd number, than it has no solution of consecutive integers. (I'm not sure if thats the same as saying if a number is a power of two or not)

[EDIT] Actually, they are the same thing.