# irreducible polynomials on the polynomial sequence

I suspect this problem is very famous and it must be studied very well. But I searched in Google and I did not find good reference. I will appreciate any answer and reference for any contribution about this question.

Firstly the motivation: We know that if $\gcd(a,b)=1$, then the sequence $an+b$ generates infinite prime numbers, when $n$ varies in the set $\mathbb{N}$. I want to generalize it for irreducible polynomials over $\Bbb{F}_q$, when $q$ is a prime power, i.e, $q=p^\alpha$, where $p$ is a prime number.

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