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=2
^{3}·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= (1^{2}+2^{3}+3^{4}+4^{5}+3^{6}+2^{7}+1^{8})+(1^{3}+1^{4}+2^{5}+1^{6}+1^{7})

2008=(7^{1}+5^{2}+3^{3})+(3^{4}+3^{5}+3^{6})+(2^{7}+2^{8}+2^{9})
- 2008 can be written as a difference of squares in several ways (e.g. 253
^{2}-249^{2})
- 2008 is the sum of the 9
^{th}, 14^{th}, and 17^{th} 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!

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Tags: 2008, math facts

This entry was posted on January 2, 2008 at 7:45 pm and is filed under Miscellaneous. You can follow any responses to this entry through the RSS 2.0 feed.
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January 3, 2008 at 5:20 pm |

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?

January 3, 2008 at 5:21 pm |

I mean to type 2008, not 200.

January 8, 2008 at 7:37 am |

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

January 8, 2008 at 7:47 am |

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

January 9, 2008 at 12:56 am |

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!)

February 1, 2011 at 4:15 am |

I mean to type 2011😀