# Irreducibility

• March 2nd 2011, 10:10 PM
Gotta
Irreducibility
If $f(x) = \sum_{j=0}^{n}a_{j}x^j\in\mathbb{Z}[x]$ is such that $f(10)$ is prime and $0\le a_{j} \le 10^{15}a_{n}$ for $j\in\left\{0, 1, \ldots n-1\right\}$, prove that $f(x)$ is irreducible.
• March 3rd 2011, 05:59 PM
Tinyboss
What have you tried? How far did you get?
• March 6th 2011, 02:50 PM
Gotta
Quote:

Originally Posted by Tinyboss
What have you tried? How far did you get?

Well, I've tried many things, and none seem to be working! Any suggestions?
• March 7th 2011, 04:37 PM
Gotta
Proved it after many failed attempts. I'd post it in here, but I doubt anyone would be interested, much like the question itself. Peace.