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 2009-09-27, 16:52 #1 Damian     May 2005 Argentina 2728 Posts 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.
 2009-09-27, 18:39 #2 Orgasmic Troll Cranksta Rap Ayatollah     Jul 2003 641 Posts
2009-09-27, 20:37   #3
Damian

May 2005
Argentina

2728 Posts

Quote:
 Originally Posted by Orgasmic Troll http://en.wikipedia.org/wiki/Von_Sta...lausen_theorem
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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