Open AccessDiophantine m-tuples for quadratic polynomials
Author(s) -
Ana Jurasić
Publication year - 2011
Publication title -
glasnik matematički
Language(s) - English
Resource type - Journals
eISSN - 1846-7989
pISSN - 0017-095X
DOI - 10.3336/gm.46.2.02
Subject(s) - mathematics , diophantine equation , polynomial , tuple , combinatorics , quadratic equation , square number , square (algebra) , quadratic function , discrete mathematics , product (mathematics) , degree (music) , mathematical analysis , geometry , physics , acoustics
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