Evaluationally relatively prime polynomials

Michelle L. Knox, Terry McDonald and Patrick Mitchell
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 21, 2015, Number 1, Pages 36–41
Full paper (PDF, 154 Kb)

Details

Authors and affiliations

Michelle L. Knox
Department of Mathematics, Midwestern State University
Wichita Falls, TX 76308, USA

Terry McDonald
Department of Mathematics, Midwestern State University
Wichita Falls, TX 76308, USA

Patrick Mitchell 
Department of Mathematics, Midwestern State University
Wichita Falls, TX 76308, USA

Abstract

Two polynomials from ℤ[x] are called evaluationally relatively prime if the greatest common divisor of the two polynomials in ℤ[x] is 1 and gcd(f(t); g(t)) = 1 for all t ∈ ℤ: A characterization is given for when a linear function is evaluationally relatively prime with another polynomial.

Keywords

• Relatively prime
• Polynomials
• Resultant

AMS Classification

• 11C08

References

1. Cohn, P. M. (2000) An Introduction to Ring Theory, Springer, London.
2. Niven, I., Zuckerman, H., & Montgomery. H. (1991) An Introduction to The Theory of Numbers, 5th edition, John Wiley & Sons, Inc.
3. Prasolov, V. (2004) Polynomials, Algorithms and Computation in Mathematics Vol. 11, Springer-Verlag, Berlin.