最大公因数和半公因数的基本公式

arXiv - MATH - General Mathematics Pub Date : 2024-06-22 DOI:arxiv-2407.03357

Joseph M. Shunia

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引用次数: 0

摘要

我们提出了计算最大公约数（GCD）和提取半素数质因数的新公式，只需使用基本算术运算：加法、减法、乘法、浮点除法和幂级数。我们的 GCD 公式简化了马赞蒂的一个结果，是利用我们以前工作中的克朗内克置换技术推导出来的。我们利用 GCD 公式，以及方根和阶乘算术项的最新发展，推导出了数乘 $n=pq$ 的质因数的明确表达式。

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Elementary Formulas for Greatest Common Divisors and Semiprime Factors

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 $n=pq$.

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arXiv - MATH - General Mathematics

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