Naslov
Diophantine m-tuples for quadratic polynomials

Autori
Jurasić, Ana

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Electronic Notes in Discrete Mathematics / Elsevier (ur.). - / - , 2013, 21-25

Skup
Erdös Centennial

Mjesto i datum
Budimpešta, Mađarska, 01.07.2013. - 05.07.2013

Vrsta sudjelovanja
Poster

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Diofantove m-torke; polinomi
(Diophantine m-tuples; polynomials)

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA