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摘 要
婆什迦罗是印度古代和中世纪最伟大数学家和天文学家, 她在数学方面成就对于古印度数学发展颇为关键。 她对于不定方程有着尤其爱好, 最有独创性成就是对婆罗摩笈多相关佩尔（Pell）方程特殊解法进行改善, 将其变为通常解法并称之为循环法（Chakravala方法）。 佩尔方程是最古老数论方程之一, 它作为二次不定方程经典代表一直深受着各界数论研究者高度关注。 婆什迦罗对于佩尔方程求解方法较为巧妙, 但因为她并没有做出具体求解和证实过程, 所以此方法并未被欧洲以后学者们过多关注。
本论文关键工作是:
1. 对婆什迦罗对佩尔方程求解方法进行研究, 求证Chakravala方法可行性和相关此方法部分论证。
2. 以佩尔方程为代表二次不定方程在现今数论研究中求解方法, 和佩尔方程应用, 并探讨这些方法中有没有对婆什迦罗求解方法借鉴。
关键词: 婆什迦罗, 佩尔方程, 求解方法
Abstract
Bhāskara ,as the greatest mathematician and astronomer in India ancient and medieval times, his mathematics achievements are important to the ancient Indian mathematics development. To volatile equation he shows a special interest in it, what the most creative achievement is the improvement to the special solution of Pell equation, he turned it to a general solution and called it Chakravala method. Pell equation is one of the most ancient number theory equations, researchers has high attention on it fot it is a classic representative of Secondary diophantine equation. Bhāskara has a clever way to slove the Pell equation, but because of he didn’t give a detailed solution and proof process,this method didn’t owned too much attention by Scholars in Europe .
The aims of this passage are as follow:
the special solution of Pell equation given by Bhāskara,and proving The feasibility of Chakravala method and the relevant some demonstration .
equation, as a representative of the secondary diophantine equation in today in the study of number theory method, we can figure out whether these methods have references to the solution given by Bhāskara.
Keywords: Bhāskara; Pell equation; the solution
目 录
1 引 言 1
论文选题背景、 目标和意义 1
相关理论 1