Timeline for Solution to $ \sum (-1)^k \binom{n}{k} \alpha_k = b_n$?
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 12, 2010 at 4:14 | comment | added | mingming | Dear Mr. Yuan: Thank you very much. Could you use Bezout Lemma to write down the solution for n=3? I want to check it with my original solution. Best! | |
| Apr 12, 2010 at 4:10 | comment | added | Qiaochu Yuan | Once more, mingming, that is not the question you originally asked. My understanding of the question you are currently asking is that you can write down a general solution by repeated use of Bezout's lemma. | |
| Apr 12, 2010 at 1:56 | comment | added | mingming | I hope the reciprocity formular will work here for bigger n. | |
| Apr 12, 2010 at 1:54 | comment | added | mingming | You can use elementary number theory method to solve this three variable Dioph. equation. But when n turn out to be 4,5,6, how can we write down a general solution? | |
| Apr 12, 2010 at 1:51 | comment | added | mingming | Thank you very much for your answer! Suppose alpha_{0}=0 , when n=2, it is 2alpha_{1}-alpha_{1}=-b_{2} If we take b_{2} to be a given number, this is a first degree Diophantine Equation, we know how to solve it using elementary number theory, right? But when n=3, take b_{3} to be a given number, alpha_{0}=0, could you write down a general solution to this Dioph. equation? | |
| Apr 12, 2010 at 1:25 | history | edited | Qiaochu Yuan | CC BY-SA 2.5 |
added 123 characters in body
|
| Apr 12, 2010 at 1:19 | history | answered | Qiaochu Yuan | CC BY-SA 2.5 |