Naslov
On the regularity of the D(4)-quadruples in Z[i][X]

Autori
Bujačić Babić, Sanda

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

Skup
Conference on Diophantine m-tuples and related problems III

Mjesto i datum
Zagreb, Hrvatska, 14.09.2022. - 16.09.2022

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Diophantine m-tuples, polynomials

Sažetak
A set {;a, b, c, d}; of four distinct nonzero polynomials in Z[i][X] is called a Diophantine D(4)-quadruple if the product of any two of its distinct elements increased by 4 is a square of a polynomial in Z[i][X]. In this work, we prove that every polynomial D(4)-quadruple in Z[i][X] is regular, or in other words that the equation (a+b- c-d)^2 = (ab+4)(cd+4) holds for every polynomial {;a, b, c, d}; D(4)-quadruple in Z[i][X]. Moreover, we compare the strategies used in this case with the cases of polynomial Diophantine quadruples in R[X] and C[X] and point out some differences and approaches.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA