I thought I'd have no trouble, but my brain seems to be substandard today. Can someone give the easy counting argument that shows the existence of irreducible polynomials of degree n over the finite field F_p? Not the one using splitting fields of x^(p^n)-x, nor the one that gives the explicit formula for the number of irreducibles but requires Mobius inversion. I was sure there was an easy nonzero lower bound on the number of irreducible polynomials, but darned if I can think of it. --Michael Kleber kleber@brandeis.edu