Timeline for Existence of an integer coefficients polynomial with prescribed bounds on [0,4]
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 6 at 21:59 | vote | accept | Yanlong Hao | ||
| Feb 14 at 15:54 | answer | added | Peter Mueller | timeline score: 3 | |
| Feb 14 at 0:02 | comment | added | Yanlong Hao | @PeterMueller Thanks for asking. The $L_\infty$ bounds here is $\infty$. Even considering the function g(x)=xf(x), the possible $L_\infty$ bounds after shift down is possible close to 2.5. Hence it is related but does not answer the question.. | |
| Feb 13 at 22:57 | comment | added | Peter Mueller | @Yanlong Hao Doesn't the technique in David Speyer's answer of your very similar previous question mathoverflow.net/questions/458834 apply here? | |
| Feb 13 at 17:32 | comment | added | Daniel Weber | Because $f(1), f(2), f(3), f(4)$ must actually be extrema, we can get the value $\mod (x-1)^2 (x-2)^2 (x-3)^2 (x-4)^2$ | |
| Feb 13 at 17:25 | comment | added | Daniel Weber | We have $f(1), f(2), f(3), f(4) \in \{0, 1\}$, so there are at most 16 possibilities to $f(x) \mod (x-1)(x-2)(x-3)(x-4)$. This modulus must also have integer coefficients (because $(x-1)(x-2)(x-3)(x-4)$ is monic), and checking all the possibilities, it must be either $0$ or $1$. | |
| Feb 13 at 14:02 | history | asked | Yanlong Hao | CC BY-SA 4.0 |