Naslov
Diophantine m-tuples

Autori
Kazalicki, Matija

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

Izvornik
Antalya Algebra Days XX / - , 2018, 11-11

Skup
Antalya Algebra Days XX

Mjesto i datum
Şirince, Turska, 16.05.2018. - 20.05.2018

Vrsta sudjelovanja
Pozvano predavanje

Vrsta recenzije
Podatak o recenziji nije dostupan

Ključne riječi
Diophantine m-tuples

Sažetak
A rational Diophantine $m$-tuple is a set of $m$ nonzero rationals such that the product of any two of them increased by $1$ is a perfect square. The first rational Diophantine quadruple was found by Diophantus, while Euler proved that there are infinitely many rational Diophantine quintuples. In 1999, Gibbs found the first example of a rational Diophantine sextuple. In the first part of the talk, we'll describe two constructions of infinite families of rational Diophantine sextuples and discuss some open problems. In the second part of the talk, we'll present the formula for the number of Diophantine quadruples over finite fields. Surprisingly, the Fourier coefficients of modular forms appear in the formula. This is joint work with A. Dujella, M. Mikic and M. Szikszai.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA