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Elementary Formulas for Greatest Common Divisors and Semiprime Factors
Joseph M. Shunia
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 semiprime…
Polynomial quotient rings and Kronecker substitution for deriving combinatorial identities
Joseph M. Shunia
We introduce a new approach for generating combinatorial identities and formulas by the application of Kronecker substitution to polynomial expansions within quotient rings. Our ma…
A Polynomial Ring Connecting Central Binomial Coefficients and Gould's Sequence
Joseph M. Shunia
We establish a novel connection between the central binomial coefficients and Gould's sequence through the construction of a specialized multivariate polynomial quo…
Arithmetic Terms for Multinomial Coefficient Sums
Joseph M. Shunia, Lorenzo Sauras-Altuzarra
We construct arithmetic terms representing the partial sums of binomial coefficients, and we extend these results to obtain arithmetic terms representing the multisections of binom…