Polynomials which take Gaussian integer values at Gaussian integers Academic Article uri icon

abstract

  • A factorial set for the Gaussian integers is a set G = {g1, g2 ... gn} of Gaussian integers such that G(z) = Πk (z - gk) gk takes Gaussian integer values at Gaussian integers. We characterize factorial sets and give a lower bound for max∥z∥2= n π ∥ G(z)∥. It is conjectured that there are infinitely many factorial sets. A Gaussian integer valued polynomial (GIP) is a polynomial with the title property. A bound similar to the above is given for max∥z∥2=n ∥ G(z)∥ if G(z) is a GIP. There is a relation between factorial sets and testing for GIP's. We discuss this and close with some examples of factorial sets, and speculate on how to find more. © 1977.

author list (cited authors)

  • Hensley, D.

citation count

  • 3

publication date

  • November 1977