beatty sequences 1elementary number theory 1irrational numbers 1iterated sequences 1membership criteria 1
From the 1 of 3 linked papers with an AI index.
3 papers
math.NT2026
A Note on Iterated Beatty Sequences
Mohsen Khani, Ali N. Valizadeh, Afshin Zarei
The paper provides an elementary number‑theoretic criterion that exactly characterizes when a natural number belongs to the nth iterate of a Beatty sequence with irrational modulus…
math.LO2025
A Tame Generic Structure with Non-Algebraic Geometric Closure
Somaye Jalili, Massoud Pourmahdian, Ali N. Valizadeh
By providing a procedure to apply Hrushovski's amalgamation method to the setting of classes of infinite structures, we introduce the notion of \textit{paracollapsed} structures. W…
math.LO2025
Fibonacci Numbers and Model-Complete Axiomatization of Presburger Arithmetic Expanded with a Beatty Sequence
Mohsen Khani, Ali N. Valizadeh, Afshin Zarei
We introduce a recursive theory that completely axiomatizes the structure where is the function that maps each to the integer part of $…