Speaker
Ana Jurasić
(Faculty of Mathematics, University of Rijeka)
Description
For a non-zero element $n\in \mathbb{Z}[X]$, a set of $m$ distinct non-zero elements from $\mathbb{Z}[X]$, such that the product of any two of them increased by $n$ is a square of an element of $\mathbb{Z}[X]$, is called a Diophantine $m$-tuple with the property $D(n)$ or simply a $D(n)$-$m$-tuple in $\mathbb{Z}[X]$. We prove that there does not exist a $D(2X+1)$-quadruple in $\mathbb{Z}[X]$, which is one counterexample for the thesis that $n\in\mathbb{Z}[X]$ is representable as a difference of squares of polynomials if and only if there exists $D(n)$-quadruple in $\mathbb{Z}[X]$.
Primary authors
Ana Jurasić
(Faculty of Mathematics, University of Rijeka)
Zrinka Franušić
(Department of Mathematics, Faculty of Science, University of Zagreb)
