Timeline for Irreducibility of a polynomial when the sum of its coefficients is prime
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 8, 2020 at 1:48 | answer | added | R. van Dobben de Bruyn | timeline score: 5 | |
| Jul 7, 2020 at 17:07 | review | Close votes | |||
| Jul 12, 2020 at 3:01 | |||||
| Jul 7, 2020 at 17:03 | comment | added | Francesco Polizzi | @R.vanDobbendeBruyn: in fact no, and I am not claiming that this is a proof of anything. For a counterexample (if exists) we must have either $\alpha+\beta+\gamma$ or $u+v$ invertible in $\mathbb{Z}$, and the other quantity an odd prime number. Moreover, the four quantities $$\alpha u, \quad \alpha v + \beta u, \quad \beta v + \gamma u, \quad \gamma v$$ must be all non-negative. | |
| Jul 7, 2020 at 16:57 | comment | added | R. van Dobben de Bruyn | @FrancescoPolizzi: do we know anything about positivity of the factors? | |
| Jul 7, 2020 at 16:26 | comment | added | Francesco Polizzi | The sum of the coefficients of $$(\alpha x^2 + \beta x + \gamma)(ux +v)$$ is $$(\alpha+\beta+ \gamma)(u+v).$$ | |
| Jul 7, 2020 at 16:08 | review | First posts | |||
| Jul 7, 2020 at 17:40 | |||||
| Jul 7, 2020 at 16:02 | history | asked | 芹沢五郎 | CC BY-SA 4.0 |