Speaker
Sanda Bujačić Babić
(Fakultet za matematiku, Sveučilište u Rijeci)
Description
A set $\{a, b, c, d\}$ of four distinct non-zero polynomials in $\mathbb{R}[X]$, which are not all constants, is called a polynomial $D(4)$-quadruple in $\mathbb{R}[X]$ if the product of any two of its distinct elements, increased by 4, is a square of a polynomial in $\mathbb{R}[X]$.
We prove some properties of these sets, and to tackle the problem of regularity of polynomial $D(4)$-quadruples in $\mathbb{R}[X]$, we investigate whether the equation $$(a+b-c-d)^2=(ab+4)(cd+4)$$ is satisfied by each such polynomial $D(4)$-quadruple in $\mathbb{R}[X]$. Our earlier research focused on the regularity of the polynomial $D(4)$-quadruple in $\mathbb{Z}[i][X]$, and we now compare these results with the recent findings from $\mathbb{R}[X]$.
Primary author
Sanda Bujačić Babić
(Fakultet za matematiku, Sveučilište u Rijeci)
