12 papers
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…
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 previ…
Two-colorings of finite grids: variations on a theorem of Tibor Gallai
Bogdan Dumitru, Mihai Prunescu
A celebrated but non-effective theorem of Tibor Gallai states that for any finite set of and for any finite number of colors there is a minimal such that no colo…
Arithmetic closed forms count the Mersenne primes, the Fermat primes and the twin-prime pairs
Mihai Prunescu
We construct closed forms that generate with repetitions all Mersenne primes, respectively all Fermat primes, all twin-prime pairs and all Sophie Germain primes. Also, we construct…
Elementary closed-forms for non-trivial divisors
Mihai Prunescu, Joseph M. Shunia
We present several elementary closed-forms that express a non-trivial divisor for every composite integer . Each closed-form consists of a fixed number of elementary arithme…
Polynomial Fingerprinting for Trees and Formulas
Mihai Prunescu
To cater to the needs of (Zero Knowledge) proofs for (mathematical) proofs, we describe a method to transform formal sentences in 2x2-matrices over multivariate polynomials with in…