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A diophantine problem from calculus.
- Source :
-
Journal of Number Theory . Aug2015, Vol. 153, p354-363. 10p. - Publication Year :
- 2015
-
Abstract
- A univariate polynomial f ( x ) is said to be nice if all of its coefficients as well as all of the roots of both f ( x ) and its derivative f ′ ( x ) are integers. The known examples of nice polynomials with distinct roots are limited to quadratic polynomials, cubic polynomials, symmetric quartic polynomials and, up to equivalence, only a finite number of nonsymmetric quartic polynomials and one quintic polynomial. In this paper we find parametrized families of nice nonsymmetric quartic polynomials with distinct roots, as well as infinitely many nice quintic and sextic polynomials with distinct roots. [ABSTRACT FROM AUTHOR]
- Subjects :
- *POLYNOMIALS
*INTEGERS
*MATHEMATICS
*CALCULUS
Subjects
Details
- Language :
- English
- ISSN :
- 0022314X
- Volume :
- 153
- Database :
- Academic Search Index
- Journal :
- Journal of Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 101935358
- Full Text :
- https://doi.org/10.1016/j.jnt.2015.01.010