We consider absolutely irreducible polynomials f∈Z[x,y] with
degx(f)=m, degy(f)=n and height H. We show that for any prime p
with p>cmnH2mn+n−1 the reduction fmodp 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>H2m.Comment: Latex, 7 page