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Let $\mathcal{A}$ and $\mathcal{B}$ be sets of polynomials of degree $n$ overa finite field. We show, that if $\mathcal{A}$ and $\mathcal{B}$ are largeenough, then $A+B$ has an irreducible divisor of large degree for some$A\in\mathcal{A}$ and $B\in \mathcal{B}$.

On divisors of sums of polynomials