ASKSAGE: Sage Q&A Forum - Individual question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Tue, 27 Aug 2019 04:07:28 -0500Could someone explain this theorem from von Staudt?https://ask.sagemath.org/question/47311/could-someone-explain-this-theorem-from-von-staudt/This is an extract from Paulo Ribenboim: 13 lectures on Fermats last theorem on page 105.
'In 1845, von Staudt determined some factors of the numerator N_2k. Let 2k = k1*k2 with gcd(k1,k2)= 1 such that p|k2 if and only if p|D_2k'. Where N_2k and D_2k are the numerators and denominators of Bernoulli number B_2k.
So I've actually used the result of this theorem for some other proof, but looking back at it I find it is not true. For example when 2k=74, then we can take k2=37. If we take p=37, we see that 37|k2=37 and so 37 must divide the denominator D_74 but D_74=6. Im not sure what I'm missing here. Maybe, I have misinterpreted the theorem. Could someone clear this up for me.Tue, 30 Jul 2019 07:52:34 -0500https://ask.sagemath.org/question/47311/could-someone-explain-this-theorem-from-von-staudt/Comment by jipilab for <p>This is an extract from Paulo Ribenboim: 13 lectures on Fermats last theorem on page 105.
'In 1845, von Staudt determined some factors of the numerator N_2k. Let 2k = k1*k2 with gcd(k1,k2)= 1 such that p|k2 if and only if p|D_2k'. Where N_2k and D_2k are the numerators and denominators of Bernoulli number B_2k.
So I've actually used the result of this theorem for some other proof, but looking back at it I find it is not true. For example when 2k=74, then we can take k2=37. If we take p=37, we see that 37|k2=37 and so 37 must divide the denominator D_74 but D_74=6. Im not sure what I'm missing here. Maybe, I have misinterpreted the theorem. Could someone clear this up for me.</p>
https://ask.sagemath.org/question/47311/could-someone-explain-this-theorem-from-von-staudt/?comment=47610#post-id-47610Could you explain how your question could be related to Sage? Otherwise, there are other platforms where such theoretical questions are welcome.Tue, 27 Aug 2019 04:07:28 -0500https://ask.sagemath.org/question/47311/could-someone-explain-this-theorem-from-von-staudt/?comment=47610#post-id-47610