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Old 2012-01-01, 11:24   #1
10metreh
 
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Default Happy 2*2*503!

Happy New Year everyone!

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Old 2012-01-02, 19:11   #2
ATH
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Happy New Year!

2012 = 29 + 113 + 132 = 1 + 28 + 33 + 123 = 1 + 113 + 142 + 222 = 22 + 63 + 82 + 123 = 24 + 35 + 36 + 45

Last fiddled with by ATH on 2012-01-02 at 19:12
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Old 2012-01-02, 19:38   #3
Batalov
 
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2012 is palindromic in bases 14, 17 and 30.
Happy New Year!

and surely in bases 502, 1005, 2011 or any b>2012 :-)

Last fiddled with by Batalov on 2012-01-02 at 19:51
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Old 2012-01-02, 20:41   #4
ATH
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Here are some with the same exponent:

2012 = 22+62+262+362 = 22+102+122+422 = 32+72+272+352 = 52+132+272+332 = 62+142+222+362



22012-1 = 3*5*6037*10061*5798167517*350862114989 * (2503-1) * C424

2503-1 = 3213684984979279*12158987054135300783*1873030665061080894263*357801561527383951750371336247776228772287580084037416747290336593974702826921943012497755232377

Last fiddled with by ATH on 2012-01-02 at 20:41
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Old 2012-01-02, 20:52   #5
Batalov
 
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Quote:
Originally Posted by ATH View Post
22012-1 = 3*5*6037*10061*5798167517*350862114989 * (2503-1) * C424
...but 2^1006+1 admits an Aurifeuillian factorization, so...
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Old 2012-01-04, 11:29   #6
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Quote:
Originally Posted by 10metreh View Post
Happy New Year everyone!

Glad we're alive.

Us Brits (Tom, Paul and me) are in the process of organizing a piss-up in the brewery ATM, with predictably little success.

I'm sure You, Flatlander and Lavalamp (to name but three) would be welcome as well.

David
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