Irreducibility

**Gotta** · March 2nd 2011, 10:10 PM

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.

**Tinyboss** · March 3rd 2011, 05:59 PM

What have you tried? How far did you get?

**Gotta** · March 6th 2011, 02:50 PM

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?

**Gotta** · March 7th 2011, 04:37 PM

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.

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