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Old 2009-09-27, 16:52   #1
Damian
 
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Default Bernoulli Number's conjeture?

Is this a known bernoulli number conjeture/theorem?:
The denominators of B_n (when expressed as an irreducible fraction), doesn't contain as a factor powers of prime numbers (ex. isn't divided by 5^2)

Example:

B_2 = \frac{1}{6}
6 = 2\cdot3

B_4 = \frac{-1}{30}
30 = 2\cdot3\cdot5

B_{24} = \frac{-236364091}{2730}
2730 = 2\cdot3\cdot5\cdot7\cdot13

I know Ramanujan proved that the denominator contain 2 and 3 as a factor one and only once, but I hadn't heard that any prime on the factorization of the denominator happens only once.
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Old 2009-09-27, 18:39   #2
Orgasmic Troll
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http://en.wikipedia.org/wiki/Von_Sta...lausen_theorem
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Old 2009-09-27, 20:37   #3
Damian
 
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Quote:
Originally Posted by Orgasmic Troll View Post
Thank you!
It's very interesting.
I would be interested in any related information to this.

It seems it doesn't work for numerators, as I run on wxMaxima:
factor(num(bern(50)));

it returned:
5^2*417202699*47464429777438199
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