A. Filipin

activity

20172022

most citedThe extension of some D(4)-pairs

1 citations · 2 across the 4 of their papers we have counts for

collaborators

4 papers

math.NT2022★ 1 cited

Pell or Pell-Lucas numbers as concatenations of two repdigits in base $b$

Kouessi Norbert Adedji, Alan Filipin, Salah Eddine Rihane +1

Let $b$ be a positive integer such that $2 \leq b \leq 10$ . In this study, we find all Pell or Pell-Lucas numbers as concatenations of two repdigits in base $b$ . As a corollary, it…

math.NT2020

The extension of the $D (- k)$ -pair ${k, k + 1}$ to a quadruple

Nikola Adžaga, Alan Filipin, Yasutsugu Fujita

Let $k$ be a positive integer. In this paper, we prove that if ${k, k + 1, c, d}$ is a $D (- k)$ -quadruple with $c > 1$ , then $d = 1$ .

math.NT2019

On the extensions of the Diophantine triples in Gaussian integers

Nikola Adžaga, Alan Filipin, Zrinka Franušić

A Diophantine $m$ -tuple is a set of $m$ distinct integers such that the product of any two distinct elements plus one is a perfect square. In this paper we study the extensibility…

math.NT2017★ 1 cited

The extension of some D(4)-pairs

Alan Filipin

In this paper we illustrate the use of the results from [1] proving that $D (4)$ -triple ${a, b, c}$ with $a < b < a + 57 a$ has a unique extension to a quadruple with a larg…

Pell or Pell-Lucas numbers as concatenations of two repdigits in base b

The extension of the D(−k)-pair {k,k+1} to a quadruple

On the extensions of the Diophantine triples in Gaussian integers

The extension of some D(4)-pairs

Pell or Pell-Lucas numbers as concatenations of two repdigits in base $b$

The extension of the $D (- k)$ -pair ${k, k + 1}$ to a quadruple