Timeline for When do binomial coefficients sum to a power of 2?
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 10, 2022 at 0:09 | vote | accept | John D. Cook | ||
| Jan 5, 2022 at 18:31 | comment | added | Terry Tao | Irreducibility over the integers is generic behavior for polynomials, see e.g., mathoverflow.net/questions/60101/… . The height of these polynomials grows exponentially in $n$, and the probability of reducibility is inversely proportional to height, so this irreducibility observation is not extremely surprising. | |
| Jan 5, 2022 at 18:19 | comment | added | Max Alekseyev | Quite remarkably, for a fixed even $n$, $S(N,n)$ as a polynomial in $N$ appears to be irreducible. I've verified this for all even $n\leq 1000$. | |
| Jan 3, 2022 at 8:19 | answer | added | Brian Hopkins | timeline score: 25 | |
| Jan 2, 2022 at 22:17 | answer | added | Max Alekseyev | timeline score: 18 | |
| Jan 2, 2022 at 3:26 | answer | added | John D. Cook | timeline score: 14 | |
| Jan 2, 2022 at 1:11 | history | became hot network question | |||
| Jan 2, 2022 at 1:02 | comment | added | Max Alekseyev | The case $n=2$ reduces to finding integral points on 3 elliptic curves: $N^2 + N + 2 = 2^a M^3$ indexed by $a\in\{0,1,2\}$, with additional restriction that $M$ is a power of 2. The solutions here can be easily computed with existing software (eg., Sage) and happen to be $N\in\{0,1,2,5,90\}$. | |
| Jan 1, 2022 at 22:38 | history | edited | LSpice | CC BY-SA 4.0 |
Minor typos and TeX
|
| Jan 1, 2022 at 22:17 | comment | added | Timothy Chow | Related (but doesn't answer the question): Sum of the first k binomial coefficients for fixed n | |
| Jan 1, 2022 at 21:58 | comment | added | Timothy Chow | OEIS sequence A175542 is relevant although it does not provide any additional examples. | |
| Jan 1, 2022 at 21:41 | comment | added | Max Alekseyev | It looks like you implicitly assume $n\leq N$ as any $N<n$ gives a trivial solution as well. | |
| Jan 1, 2022 at 21:31 | history | edited | Daniele Tampieri | CC BY-SA 4.0 |
(Extremely) Minor Math Jaxing
|
| Jan 1, 2022 at 20:57 | history | edited | Martin Sleziak |
edited tags
|
|
| Jan 1, 2022 at 20:41 | answer | added | Max Alekseyev | timeline score: 24 | |
| Jan 1, 2022 at 19:37 | comment | added | Max Alekseyev | For each fixed $n>1$, the number of solutions $N$ is finite as the corresponding equation reduces to a finite number of (hyper)elliptic ones. | |
| Jan 1, 2022 at 17:06 | history | asked | John D. Cook | CC BY-SA 4.0 |