Vol. 3, No. 2, 2010

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The probability of relatively prime polynomials in $\mathbb{Z}_{p^k}[x]$

Thomas R. Hagedorn and Jeffrey Hatley

Vol. 3 (2010), No. 2, 223–232
Abstract

Let PR(m,n) denote the probability that two randomly chosen monic polynomials f, g R[x] of degrees m and n, respectively, are relatively prime. Let q = pk be a prime power. We establish an explicit formula for PR(m,2) when R = q, the ring of integers mod q.

Keywords
relatively prime polynomials
Mathematical Subject Classification 2000
Primary: 11C20, 13B25, 13F20
Milestones
Received: 11 December 2009
Revised: 25 April 2010
Accepted: 26 April 2010
Published: 11 August 2010

Communicated by Arthur T. Benjamin
Authors
Thomas R. Hagedorn
The College of New Jersey
Department of Mathematics and Statistics
P.O. Box 7718
Ewing, NJ 08628
United States
Jeffrey Hatley
The College of New Jersey
Department of Mathematics and Statistics
P.O. Box 7718
Ewing, NJ 08628
United States
Department of Mathematics and Statistics
University of Massachusetts at Amherst
Amherst, MA 01003