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Diophantine m-tuples for linear polynomials II. Equal degrees
- Source :
-
Journal of Number Theory . Oct2006, Vol. 120 Issue 2, p213-228. 16p. - Publication Year :
- 2006
-
Abstract
- Abstract: In this paper we prove the best possible upper bounds for the number of elements in a set of polynomials with integer coefficients all having the same degree, such that the product of any two of them plus a linear polynomial is a square of a polynomial with integer coefficients. Moreover, we prove that there does not exist a set of more than 12 polynomials with integer coefficients and with the property from above. This significantly improves a recent result of the first two authors with Tichy [A. Dujella, C. Fuchs, R.F. Tichy, Diophantine m-tuples for linear polynomials, Period. Math. Hungar. 45 (2002) 21–33]. [Copyright &y& Elsevier]
- Subjects :
- *POLYNOMIALS
*ALGEBRA
*APPROXIMATION theory
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 0022314X
- Volume :
- 120
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 22076195
- Full Text :
- https://doi.org/10.1016/j.jnt.2005.12.005