Irreducible Quartic Polynomials with Factorizations modulo p
Eric D. Driver, Philip A. Leonard, Kenneth S. Williams · American Mathematical Monthly · 2005
text, Dummit and Foote include the following remark [4, p. 310]: Unfortunately, there are examples of polynomials even in Z[x] which are irreducible but whose reductions modulo every ideal are reducible.... For example, the polynomial x4 + 1 is irreducible in Z[x] but is reducible modulo