Timeline for Special case of testing integer polynomials for irreducibility
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Jul 27, 2012 at 21:42 | answer | added | Igor Rivin | timeline score: 1 | |
| Jul 27, 2012 at 17:46 | comment | added | roy smith | I only know the generalized Eisenstein criterion *Van der Waerden, 2nd.ed, p76-77), essentially that if a prime q exists whose highest power dividing b is q^k, where k is not a multiple of p, and if q^k also divides a, then irreducibility follows, (assuming n=p is prime). e.g. X^5 + 12X + 4. Moreover if X^n + pX + cp^2 is irreducible, then it has a linear factor. e.g. X^6 + 3X + 9 has no root mod 5 hence is irreducible. I hope this is right, as I am a novice. | |
| Jul 27, 2012 at 16:44 | comment | added | paul garrett | An immediate special sub-case is the "Artin-Schreier" polynomials $x^p-x+a$, for $p$ prime, which are irreducible for $a\in\mathbb Z$ not divisible by $p$, because they are irreducible mod $p$. | |
| Jul 27, 2012 at 15:17 | history | asked | Joe Shipman | CC BY-SA 3.0 |