4 papers · 1 filter
On Periodic and Aperiodic Optimal Strategies in Solvency Games
Quentin Guilmant, Florian Luca, Richard Mayr +2
Solvency games are a gambling problem on infinite-state Markov decision processes in which the state represents an investor's fortune. In every round, the invest…
On the Divisibility Relation and a Generalized Erdős--Sierpiński Conjecture
Amirali Fatehizadeh, Florian Luca
For each fixed positive integer , we study the divisibility relation . We isolate an explicit regular family arising from integral quotients of shifted abundancy…
Multiplicative dependence in the sumset of multiplicative groups
Yuri Bilu, Florian Luca
Let and be finitely generated multiplicative groups of algebraic numbers such that is a finite group. We show that, up to finitely many exceptions, non-zero sums $…
Conjectural Decidability of the Skolem Problem
Florian Luca, Joël Ouaknine, James Worrell
The Skolem Problem asks to determine whether a given integer linear recurrence sequence (LRS) has a zero term. This problem, whose decidability has been open for many decades, aris…