AI 中文总结
研究两平方和\(X^{2}+Y^{2}\)的因式分解，通过线性和二次数列生成分解，关联整数\(n\)分解数与除数个数\(d(n)\)，并给出用筛法获得分解的算法。
AI 中文摘要
本文研究两平方和\(X^{2}+Y^{2}\)的因式分解。证明了存在关于\(X\)的线性和二次数列能生成因式分解及两平方和的替代分解。自然关注整数\(n\)的两平方和分解数，并将其与除数个数\(d(n)\)联系起来。最后给出用文献(1)中筛法获得这些分解的算法。
英文摘要
In this paper, we study the factorization of sums of two squares X2 + Y2. We show the existence of linear and quadratic progressions on X that generate both factorizations and alternative decompositions into sums of two squares. We are therefore naturally interested in the number of decompositions into sums of two squares of an integer n and relate it to its number of divisors d(n). Finally, we present an algorithm to obtain these decompositions using the sieve introduced in (1).
Comments30 pages
