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math.LO2026
On Integer-Division Bases for the Kalmár Elementary Functions
Joseph M. Shunia
Prunescu, Sauras-Altuzarra, and Shunia asked whether addition, totalized integer division, and base-two exponentiation form a substitution basis for the Kalmár elementary functions…
math.LO2026
Undecidability, Chaos and Universality in Arithmetic Terms
Gabriel Istrate, Mihai Prunescu, Joseph M. Shunia
Arithmetic terms are finite fixed compositions of additions, subtractions, multiplications, divisions with remainder and exponentiations, containing variables interpreted as natura…
math.LO2025
A Minimal Substitution Basis for the Kalmár Elementary Functions
Mihai Prunescu, Lorenzo Sauras-Altuzarra, Joseph M. Shunia
We show that the class of Kalmár elementary functions can be inductively generated from the addition, the integer remainder, and the base-two exponentiation, hence improving previo…