We consider absolutely irreducible polynomials f ∈ Z[x, y] with deg x f = m, deg y f = n and height H. We show that for any prime p with2 •H 2mn+n−1 the reduction f mod p is also absolutely irreducible. Furthermore if the Bouniakowsky conjecture is true we show that there are infinitely many absolutely irreducible polynomials f ∈ Z[x, y] which are reducible mod p where p is a prime with p ≥ H 2m .
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