1) least positive integer solution
最小正整数解
1.
Giving a criterion of the least positive integer solution to general binary quadratic Diophantine equation, and the least positive integer solution to several binary quadratic Diophantine equations and Pell equations, generalizing two results in and .
给出一般二元二次不定方程最小正整数解的一个判定准则 ,确定了几类二元二次不定方程和Pell方程的最小正整数解 ,推广了 [1 ]、[2 ]中的两个结
2) smallest positive integer
最小正整数
1.
Problem of the smallest positive integer related to Gaussian integer;
一个关于高斯整数的最小正整数问题
3) miniinteger solution
最小整数解
1.
In order to solve the miniinteger solution of Pell equations,we give algorithm of the Maple by using the continued fraction and also get the general program.
利用连分数的性质从理论上对Pell方程的最小整数解给出了一种算法,并利用Maple数学软件给出了用相应的求解Pell方程最小整数解的通用程序。
4) the most predigest positive integer coefficient solution
最简正整数系数解
5) minimal positive slution
最小正解
6) positive integral solution
正整数解
1.
With a recursive sequence,quadratic remainder and congruence,the diophantine equation x2-3y4=97 is proved that it has only positive integral solutions(x,y)=(10,1).
运用递归数列,同余式和平方剩余证明了不定方程x2-3y4=97仅有正整数解(x,y)=(10,1)。
2.
Let p be a prime number,using Fermat Infinite method of descent,to study the positive integral solution of the equations x~4±3px~2y~2+3p~2y~4=z~(2) and x~4±6px~2y~2-3p~2y~4=z~(2).
设p为素数,利用F erm at无穷递降法,研究方程x4±3px2y2+3p2y4=z2与x4±6px2y2-3p2y4=z2正整数解的存在性,证明该方程在p≡5(m od 12)时均无正整数解,在p≡11(m od 12)时有解且有无穷多组正整数解,获得方程无穷多组正整数解的通解公式和方程的部分正整数解。
3.
By using computer language, we get all the positive integral solution of x2±xy+y2 = P and x2±xy+y2 = 3p within the scope of arbitrarily.
讨论了方程x2±xy+y2=k的可解性,利用C语言编写出方程x2±xy+y2=p和x2±xy+y2=3P的计算程序,并获得方程在一定范围内的所有正整数解。
补充资料：正整数
即“自然数”(1159页)。
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
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