Timeline for Is $\sum\limits_{k=1}^nk^m=S_3(n)\cdot\dfrac{P_{m-3}(n)}{N_m}$ for odd $m>1,\sum\limits_{k=1}^nk^m=S_2(n)\cdot\dfrac{P_{m-2}'(n)}{N_m}$ for even $m$?
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| Dec 26, 2023 at 21:17 | history | edited | pie | CC BY-SA 4.0 |
added 176 characters in body; edited title
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| Dec 26, 2023 at 15:28 | history | edited | Daniele Tampieri | CC BY-SA 4.0 |
Formatting and minor Math Jaxing
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| Dec 26, 2023 at 14:28 | review | Close votes | |||
| Jan 4 at 3:12 | |||||
| Dec 26, 2023 at 8:30 | comment | added | Sam Hopkins | I googled “denominators of Faulhaber polynomials.” Anyways I think the question is better for MSE. You should post the answer there. | |
| Dec 26, 2023 at 6:21 | comment | added | pie | @SamHopkins the only question on my mind now is how did you find this paper | |
| Dec 26, 2023 at 6:20 | comment | added | pie | @Elaqqad Thank you for your explanations and thank you Sam Hopkins for the paper and explanation btw should I edit the question on MSE and include the answer or should I write that on answer or what ? should I delete this question? | |
| Dec 26, 2023 at 0:04 | comment | added | Elaqqad | @pie the paper in question answers completely your question. It gives you that $d_n=(n+1)q_n$ and theorem 3 shows you the exact factorization of $q_n$. It suffices to notice that $\epsilon_2=1$ when $n$ is odd $\geq 3$ which is the case, and compute $\epsilon_3$ for $n$ even for which the formula is given, it actually equals $1$ most of the time | |
| Dec 25, 2023 at 21:41 | comment | added | pie | @SamHopkins I didn't understand how this would help with my question, it took me a loot of time to semi understand that theorem. | |
| Dec 25, 2023 at 1:24 | comment | added | pie | @SamHopkins Are you sure that it contain an answer to my question ?after a quick look at it I didn't find anything about my question. | |
| Dec 25, 2023 at 1:10 | comment | added | Sam Hopkins | Denominators of Faulhaber polynomials are studied in the paper: arxiv.org/abs/1705.03857. It should contain an answer to your question. | |
| Dec 25, 2023 at 1:02 | history | edited | pie | CC BY-SA 4.0 |
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| Dec 25, 2023 at 1:00 | comment | added | pie | @SamHopkins somehow I forgot to write that $gcd \{ a_0 , a_1,\dots, a_i\} =1$ | |
| Dec 25, 2023 at 0:53 | history | edited | pie | CC BY-SA 4.0 |
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| Dec 25, 2023 at 0:51 | comment | added | pie | @SamHopkins I couldn't prove that pattern from Faulhaber's formula. | |
| S Dec 25, 2023 at 0:47 | review | First questions | |||
| Dec 25, 2023 at 5:41 | |||||
| S Dec 25, 2023 at 0:47 | history | asked | pie | CC BY-SA 4.0 |