由Pell方程及其类似方程求同余数
Congruent Numbers Via the Pell Equation and its Analogous Counterpart
摘要：
本文的目的是双重的。第一种是引入定义在值为同余数的正整数上的几个单变量多项式和二元多项式。第二个是目前的毕达哥拉斯三元组和佩尔方程$x^2-dy^2=1$加上其类似的副本$x^2-dy^2=-1$，从而产生的全等数n与任意多个素因子之间的连接。
英文摘要：
The aim of this expository article is twofold. The first is to introduce several polynomials of one variable as well as two variables defined on the positive integers with values as congruent numbers. The second is to present connections between Pythagorean triples and the Pell equation $x^2-dy^2=1$ plus its analogous counterpart $x^2-dy^2=-1$ which give rise to congruent numbers n with arbitrarily many prime factors.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
