Diophantine m-tuples for quadratic polynomials | Zendy

Ana Jurasić | Zendy

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Diophantine m-tuples for quadratic polynomials

Author(s) -

Ana Jurasić

Publication year - 2011

Publication title -

glasnik matematicki

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

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