Glasnik matematički, Vol. 46 No. 2, 2011.
Original scientific paper
https://doi.org/10.3336/gm.46.2.02
Diophantine m-tuples for quadratic polynomials
Ana Jurasic
; Department of Mathematics, University of Rijeka, Omladinska 14, 51000 Rijeka, Croatia
Abstract
In this paper, we prove that there does not exist a set with more than 98 nonzero polynomials in Z[X], such that the product of any two of them plus a quadratic polynomial n is a square of a polynomial from Z[X] (we exclude the possibility that all elements of such set are constant multiples of a linear polynomial pZ[X] such that p2|n). Specially, we prove that if such a set contains only polynomials of odd degree, then it has at most 18 elements.
Keywords
Diophantine m-tuples; polynomials
Hrčak ID:
74260
URI
Publication date:
23.11.2011.
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