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Diophantine m-tuples for quadratic polynomials (CROSBI ID 178998)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Jurasić, Ana
Diophantine m-tuples for quadratic polynomials // Glasnik matematički, 46 (2011), 2; 283-309. doi: 10.3336/gm.46.2.02
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Jurasić, Ana
engleski
Diophantine m-tuples for quadratic polynomials
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 p in Z[X] such that p^2|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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