Glasnik Matematicki, Vol. 46, No. 2 (2011), 283-309.

DIOPHANTINE m-TUPLES FOR QUADRATIC POLYNOMIALS

Ana Jurasić

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.

2000 Mathematics Subject Classification.   11C08, 11D99.

Key words and phrases.   Diophantine m-tuples, polynomials.

DOI: 10.3336/gm.46.2.02

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