I. Vukusic

activity

20202025

most citedOn a family of cubic Thue Equations involving Fibonacci and Lucas numbers

2 citations · 3 across the 6 of their papers we have counts for

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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.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…