3 papers
math.CO2025
A Lebesgue variant of the additive square problem
Ingrid Vukusic
The additive square problem is a relatively famous open problem in the area of combinatorics on words: Does there exist an infinite word over a finite alphabet, such that no two co…
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 be any imaginary quadratic integer with . 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 . In other words, they conjectured…