On the greatest common divisor of the value of two polynomials
Abstract
We show that if two monic polynomials with integer coefficients have square-free resultant, then all positive divisors of the resultant arise as the greatest common divisor of the values of the two polynomials at a suitable integer.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2016
- DOI:
- 10.48550/arXiv.1608.07936
- arXiv:
- arXiv:1608.07936
- Bibcode:
- 2016arXiv160807936F
- Keywords:
-
- Mathematics - Number Theory;
- Mathematics - Commutative Algebra;
- 11N32;
- 11C08;
- 11C20;
- 11A05;
- 13P15;
- 12E05;
- 15A03;
- 15A21
- E-Print:
- 6 pages