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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.NT2026
Prime-Interval Algebras
Joseph M. Shunia
Starting from a positive integer and no a priori information about the primes above it, we construct a polynomial quotient ring that recovers exactly the primes in fro…
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…