Abstract :
We consider absolutely irreducible polynomialsfset membership, variantZ[x, y] with degx f=m, degy f=n, and heightH. We show that for any primepwithp>[m(n+1) n2+(m+1)(n−1) m2]mn+(n−1)/2·H2mn+n−1the reductionf mod pis also absolutely irreducible. Furthermore if the Bouniakowsky conjecture is true we show that there are infinitely many absolutely irreducible polynomialsfset membership, variantZ[x, y] which are reducible mod pwherepis a prime withpgreater-or-equal, slantedH2m.
