2 citations · 3 across the 15 of their papers we have counts for
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Straight-line programs for the solutions of Pell's equation
Bogdan Dumitru, Mihai Prunescu
For nonsquare , we construct fixed straight-line programs for the least non-trivial solution of , using addition, truncated subtraction, multiplicat…
How many points does an affine algebraic set have in residue classes modulo n ?
Mihai Prunescu
We show that for every uniform family of affine algebraic sets, there is a formula in the parameters of the family and in , expressing the cardinality of the set in the ring $\m…
Short arithmetic terms for the cardinality of elliptic curves over rings of remainder classes and over finite fields
Bogdan Dumitru, Mihai Prunescu
Arithmetic terms are fixed finite compositions of addition, truncated subtraction, multiplication, integer division and exponentiation on natural numbers. We construct such terms f…
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…
On modular representations of C-recursive integer sequences
Mihai Prunescu, Joseph M. Shunia
Prunescu and Sauras-Altuzarra showed that all C-recursive sequences of natural numbers have an arithmetic div-mod representation that can be derived from their generating function.…
On arithmetic terms expressing the prime-counting function and the n-th prime
Mihai Prunescu, Joseph M. Shunia
We present the first fixed-length elementary closed-form expressions for the prime-counting function, , and the -th prime number, . These expressions are arithmetic…
Arithmetic-term representations for the greatest common divisor
Mihai Prunescu, Joseph Shunia
We construct a new arithmetic-term representation for the function gcd(a,b). As a byproduct, we also deduce a representation gcd(a,b) by a modular term in integer arithmetic.
On the representation of number-theoretic functions by arithmetic terms
Mihai Prunescu, Lorenzo Sauras-Altuzarra
We present closed forms for several functions that are fundamental in number theory and we explain the method used to obtain them. Concretely, we find formulas for the p-adic valua…
On other two representations of the C-recursive integer sequences by terms in modular arithmetic
Mihai Prunescu
An integer sequence that is defined by initial values and a linear recurrence with constant integer coefficients, can be represented by the difference of two arithmetic terms conta…