渐近分数的应用研究

A Study on the Application of Convergent

用渐近分数得到了两个结果:(1)用n～(1/2)的渐近分数表示了纯循环二次无理数α=(a+(n～(1/2)))/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x2-ny2=±A的另一解法.

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 of successive division. （2） When A is a composite number, another solution of indeterminate equations x^2-ny^2=±A is given with convergent.