渐近分数的应用研究

摘要

This study addresses convergent. The findings are as follows, （ 1 ） the convergent of √n represents the fraction composed by repetend of pure recurring quadratic irrational number α=（α＋√n）/b and arithmetic of continued fraction of ot is educed with method%用渐近分数得到了两个结果：（1）用√n的渐近分数表示了纯循环二次无理数α=（α＋√n）／b的循环节所构成的分数，从而引出了用辗转相除法给出α的连分数的算法．（2）当A为合数时，用渐近分数给出了不定方程x^2-ny^2=±A的另一解法．