engleski

Diophantine m-tuples for quadratic polynomials

The poster presents one polynomial variant of the problem of Diophantus, described by A. Jurasić [Diophantine m-tuples for quadratic polynomials, Glas. Mat. Ser. III 46 (2011), 283–309], and ilustrates that results with some examples from the paper of A. Dujella and A. Jurasić [Some Diophantine triples and quadruples for quadratic polynomials, J. Comb. Number Theory 3(2) (2011), 123–141]. We proved 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 p∈Z[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.

Diophantine m-tuples; polynomials

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