Naslov
Some recent results on polynomial Diophantine m-tuples

Autori
Filipin, Alan ; Jurasić, Ana

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

Izvornik
The 29th Journees Arithmetiques / - Deberecen, 2015, 40-40

Skup
29th Journees Arithmetiques

Mjesto i datum
Debrecen, Mađarska, 05.07.2015. - 10.07.2015

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Diophantine m-tuples; polynomials

Sažetak
Let a, b and c be non-zero polynomials with integer coefficients such that there exist three polynomials r, s and t from Z[X] such that ab-1=r^2, ac-1=s^2 and bc-1=t^2. Moreover, let d from Z[X] be a polynomial such that there exist x, y and z from Z[X] such that ad+1=x^2, bd+1=y^2 and cd+1=z^2, i.e. {;a, b, c, d}; is a D(-1 ; 1)- quadruple. In this talk we prove that d is uniquely determined by a, b and c. More precisely, the only possibilities for d are d = 0, d=-(a + b + c)+2abc+-2rst. Except that, we will also discuss some other recent results on the topic.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA