I. Vukusic

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20202025

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

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

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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}…

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

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