Zobrazeno 1 - 5
of 5
pro vyhledávání: '"Shunia, Joseph M."'
Autor:
Prunescu, Mihai, Shunia, Joseph M.
We present the first fixed-length elementary closed-form expressions for the prime-counting function, pi(n), and the n-th prime number, p(n). These expressions are represented as arithmetic terms, requiring only a fixed and finite number of elementar
Externí odkaz:
http://arxiv.org/abs/2412.14594
Autor:
Shunia, Joseph M.
We conjecture new elementary formulas for computing the greatest common divisor (GCD) of two integers, alongside an elementary formula for extracting the prime factors of semiprimes. These formulas are of fixed-length and require only the basic arith
Externí odkaz:
http://arxiv.org/abs/2407.03357
Autor:
Shunia, Joseph M.
We introduce a new approach for generating combinatorial identities and formulas by the application of Kronecker substitution to polynomial expansions within quotient rings. Our main result enables the derivation of elementary arithmetic formulas for
Externí odkaz:
http://arxiv.org/abs/2404.00332
Autor:
Shunia, Joseph M.
We present a simple formula for calculating univariate multinomial coefficients, which count the number of distinct ways to arrange a collection of $n$ items when divided into labeled groups of fixed sizes. Notably, we also introduce what appear to b
Externí odkaz:
http://arxiv.org/abs/2312.00301
Autor:
Shunia, Joseph M.
We establish a novel connection between the central binomial coefficients $\binom{2n}{n}$ and Gould's sequence through the construction of a specialized multivariate polynomial quotient ring. Our ring structure is characterized by ideals generated fr
Externí odkaz:
http://arxiv.org/abs/2312.00302