We present new formulas for computing greatest common divisors (GCDs) and extracting the prime factors of semiprimes using only elementary arithmetic operations: addition, subtraction, multiplication, floored division, and exponentiation. Our GCD formula simplifies a result of Mazzanti, and is derived using Kronecker substitution techniques from our previous work. We utilize the GCD formula, along with recent developments on arithmetic terms for square roots and factorials, to derive explicit expressions for the prime factors of a semiprime $n=pq$.
No takes yet. Share an insight, caveat, or question.
Joseph M. Shunia (2024) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: