I. Vukusic

activity

20202025

U_{n} - b^{m} = c

2 citations · 5 across the 12 of their papers we have counts for

collaborators

14 papers

math.NT2025

Bounds for sets of remainders

Omkar Baraskar, Ingrid Vukusic

Let $s (n)$ be the number of different remainders $n mod k$ , where $1 \leq k \leq ⌊ n /2 ⌋$ . This rather natural sequence is sequence A283190 in the OEIS and while some…

math.NT2025

Some Bounds Related to the $2$ -adic Littlewood Conjecture

Dinis Vitorino, Ingrid Vukusic

For every irrational real $α$ , let $M (α) = sup_{n \geq 1} a_{n} (α)$ denote the largest partial quotient in its continued fraction expansion (or $\infty$ , if unbounded). The $2$ -adic…

math.NT2023

On a simple quartic family of Thue equations over imaginary quadratic number fields

Benjamin Earp-Lynch, Bernadette Faye, Eva G. Goedhart +2

Let $t$ be any imaginary quadratic integer with $∣ t ∣ \geq 100$ . We prove that the inequality \[ |F_t(X,Y)| = | X^4 - t X^3 Y - 6 X^2 Y^2 + t X Y^3 + Y^4 | \leq 1 \] has only trivial…

math.NT2023

On sums of two Fibonacci numbers that are powers of numbers with limited Hamming weight

Ingrid Vukusic, Volker Ziegler

In 2018, Luca and Patel conjectured that the largest perfect power representable as the sum of two Fibonacci numbers is $386 4^{2} = F_{36} + F_{12}$ . In other words, they conjectured…

math.NT2023

Thue equations over $C (T)$ : The Complete Solution of a Simple quartic family

Bernadette Faye, Ingrid Vukusic, Ezra Waxman +1

In this paper we completely solve a simple quartic family of Thue equations over $C (T)$ . Specifically, we apply the ABC-Theorem to find all solutions $(x,y) \in \mathbb{C}…

math.NT2022★ 2 cited

On the Diophantine equation $U_{n} - b^{m} = c$

Sebastian Heintze, Robert F. Tichy, Ingrid Vukusic +1

Let $(U_{n})_{n \in N}$ be a fixed linear recurrence sequence defined over the integers (with some technical restrictions). We prove that there exist effectively computable c…

math.NT2021

On a cubic Family of Thue Equations involving Fibonacci Numbers and Powers of Two

Ingrid Vukusic

In this paper we completely solve the family of parametrised Thue equations \[ X(X-F_n Y)(X-2^n Y)-Y^3=\pm 1, \] where $F_{n}$ is the $n$ -th Fibonacci number. In particular, for any…

math.NT2021★ 2 cited

On a family of cubic Thue Equations involving Fibonacci and Lucas numbers

Tobias Hilgart, Ingrid Vukusic, Volker Ziegler

Let $F_{n}$ denote the $n$ -th Fibonacci number and $L_{n}$ the $n$ -th Lucas number. We completely solve the family of cubic Thue equations $(X - F_{n} Y) (X - L_{n} Y) X - Y^{3} = \pm 1$ and show tha…

math.NT2021★ 1 cited

On sums of Fibonacci numbers with few binary digits

Ingrid Vukusic, Volker Ziegler

In this paper we completely solve the Diophantine equation $F_{n} + F_{m} = 2^{a_{1}} + 2^{a_{2}} + 2^{a_{3}} + 2^{a_{4}} + 2^{a_{5}}$ , where $F_{k}$ denotes the $k$ -th Fibonacci number. In addition to comple…

math.NT2021

On a family of unit equations over simplest cubic fields

Ingrid Vukusic, Volker Ziegler

Let $a \in Z$ and $ρ$ be a root of $f_{a} (x) = x^{3} - a x^{2} - (a + 3) x - 1$ , then the number field $K_{a} = Q (ρ)$ is called a simplest cubic field. In this paper we consider the fam…

math.NT2021

Consecutive tuples of multiplicatively dependent integers

Ingrid Vukusic, Volker Ziegler

This paper is concerned with the existence of consecutive pairs and consecutive triples of multiplicatively dependent integers. A theorem by LeVeque on Pillai's equation implies th…

math.NT2020

On a variant of Pillai's problem with transcendental numbers

Robert Tichy, Ingrid Vukusic, Daodao Yang +1

In this paper, we study the asymptotic behaviour of the number of solutions $(m, n) \in N^{2}$ to the inequality $∣ α^{n} - β^{m} ∣ \leq x$ when $x$ tends to infinity. Here $α,…

math.NT2020

Integers representable as differences of linear recurrence sequences

Robert Tichy, Ingrid Vukusic, Daodao Yang +1

Let ${U_{n}}_{n \geq 0}$ and ${V_{m}}_{m \geq 0}$ be two linear recurrence sequences. We establish an asymptotic formula for the number of integers $c$ in the range $[- x, x]$ which…

math.NT2020

Integers representable as differences of linear recurrence sequences

Daodao Yang

Let ${U_{n}}_{n ⩾ 0}$ and ${G_{m}}_{m ⩾ 0}$ be two linear recurrence sequences defined over the integers. We establish an asymptotic formula for the number of integ…

Bounds for sets of remainders

Some Bounds Related to the 2-adic Littlewood Conjecture

On a simple quartic family of Thue equations over imaginary quadratic number fields

On sums of two Fibonacci numbers that are powers of numbers with limited Hamming weight

Thue equations over C(T): The Complete Solution of a Simple quartic family

On the Diophantine equation Un​−bm=c

On a cubic Family of Thue Equations involving Fibonacci Numbers and Powers of Two

On a family of cubic Thue Equations involving Fibonacci and Lucas numbers

On sums of Fibonacci numbers with few binary digits

On a family of unit equations over simplest cubic fields

Consecutive tuples of multiplicatively dependent integers

On a variant of Pillai's problem with transcendental numbers

Integers representable as differences of linear recurrence sequences

Integers representable as differences of linear recurrence sequences

Some Bounds Related to the $2$ -adic Littlewood Conjecture

Thue equations over $C (T)$ : The Complete Solution of a Simple quartic family

On the Diophantine equation $U_{n} - b^{m} = c$