## 2008!

by

What are some fun facts about 2008? I’m sure there are many, but here are a couple that come to mind:

• 2008 has only two prime divisors (2 and 251, since 2008=23·251)
• 2008 can be written as the sum of 251 consecutive integers:
(-117)+(-116)+(-115)+…+131+132+133
• 2008 can be written as the sum of of 16 consecutive positive integers:
118+119+120+…+132+133
• I can’t find a way in which 2008 can be written as a sum of increasing powers in a particularly elegant fashion, but I did find that:
2008= (12+23+34+45+36+27+18)+(13+14+25+16+17)
2008=(71+52+33)+(34+35+36)+(27+28+29)
• 2008 can be written as a difference of squares in several ways (e.g. 2532-2492)
• 2008 is the sum of the 9th, 14th, and 17th Fibonacci Numbers (34+377+1597)

No doubt there are many other ways to make 2008, or fun facts about the number — post the facts or links to similar pages here!

Tags: ,

### 6 Responses to “2008!”

1. Sol Lederman Says:

200 can be written as the sum of three cubes in two ways. One is 10^3+10^3+2^3. What’s the other?

2. Sol Lederman Says:

I mean to type 2008, not 200.

3. Mike Says:

Hi

There are some nice results there – I especially like the ones involving sums of consecutive integers. I wrote a similar post to this a little while ago if you are interested -

http://www.walkingrandomly.com/?p=40

cheers,
Mike

4. Walking Randomly » What is interesting about the number 2008? Says:

[...] have just discovered another blog post that has some fun facts about 2008 over at 360 – my favorite of which [...]

5. Ξ Says:

Sol, I played around with it on Excel and came up with 4^3+6^3+12^3. Great problem! Interestingly, factoring 2^3 out of each term leads to 2008=2^3*[1^3+5^3+5^3] but also 2^3*[2^3+3^3+6^3], which really just says that the factor 251 can be written as the sum of cubes in two different ways. Cool!

Mike, thanks for the link! I followed it and really enjoyed your post (and the others on your blog!)

6. direksiyon Says:

I mean to type 2011