1. ## 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.

2. What have you tried? How far did you get?

3. 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?

4. 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.