1) quadratic residue function (QRF)
平方剩余函数
2) square residues
平方剩余数
1.
On some mean value formulas of the square residues;
关于平方剩余数的几个均值公式
3) Surplus function
剩余函数
1.
Surplus function variational quantum Monte Carlo (SFVMC) approach for the electronic excited state has been established in this paper.
提出了用于电子激发态的剩余函数变分量子Ｍｏｎｔｅ Ｃａｒｌｏ（ＳＦＶＭＣ）方法。
2.
The solutions included treating bracket,calculating the surplus function,changing string into numeric and so on.
其中包括括号处理、计算剩余函数、字符串转换成数值等问题的处理方法。
4) residual function
剩余函数
1.
Based on the principle of the residual function in statistical mechanics and derived from a new concise reduced virial equation of state for ammonia which had been presented by our research group in 1998, the new correlations for determining two energy derivative properties-enthalpy and entropy of ammonia have been proposed in this paper.
本文根据统计力学与热力学剩余函数理论，结合本课题组已建立的氨工质新状态方程，推导出一则可供精确确定氨的焓（ｈ）与熵（ｓ）参数的新关联式。
5) quadratic remainder
平方剩余
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.
This paper proves that the Diophantine Equation has only positive integral solution with the methods of recursive sequence,congruence and quadratic remainder.
利用一种初等的证明方法,即递推序列、同余式和平方剩余的方法,对不定方程x2-11y4=38的正整数解进行了研究,证明了不定方程x2-11y4=38仅有正整数解(x,y)=(7,1)。
3.
Defined are the characters of quadratic remainder while the arithmetic is provided for choosing X coordinate of base point G .
结合椭圆曲线域参数属性 ,讨论了平方剩余的定义、性质 ,完整地设计出选取基点G的X坐标的算法 。
6) quadratic residue
平方剩余
1.
In this paper,the author has proved that the Diophantine equation x3+64=21y2 has only an integer solution(x,y)=(-4,0),(5,±3) and then gives all integer solution of x3+64=21y2 by using the elementary methods such as recursive sequence,congruent fomula and quadratic residue.
利用递归数列、同余式和平方剩余几种初等方法,证明了不定方程x3+64=21y2仅有整数解(x,y)=(-4,0),(5,±3);给出了x3+64=21y2的全部整数解。
2.
In this paper,the author has proved that the Diophantine equation x3+27=7y2 has only an integer solution(x,y)=(-3,0),(1,±2) and then gives all integer solution of x3+27=7y2 by using the elementary methods such as recursive sequence,congruent fomula and quadratic residu
利用递归数列、同余式和平方剩余几种初等方法,证明了不定方程x3+27=7y2仅有整数解(x,y)=(-3,0),(1,±2);给出了x3+27=7y2的全部整数解。
3.
In this paper the author has proved that the Diophantine equation x3+27=26y2 has only integer solutions(-3,0),(-1,±1),(719,±3781)with the methods of recurrent sequence,congruence and quadratic residue.
利用递归数列、同余式和平方剩余证明了不定方程x3+27=26y2仅有整数解(-3,0),(-1,±1),(719,±3781)。
补充资料：平方剩余
假设p是素数，a是整数。 如果存在一个整数x使得x^2≡a(mod p) （即x^2-a可以被p整除）， 那么就称a在p的剩余类中是平方剩余的。
欧拉定理说：a平方剩余当且仅当 a^{(p-1)/2}≡1 (mod p).
在{1,2,...,p-1}中恰好有（p-1）/2 个数是平方剩余的。
拉格朗日符号： 【a/p】=1 (相应的，-1) 如果 a是平方剩余(相应的， 如果 a不是平方剩余）。
高斯著名的二次互反律告诉我们：假设p和q都是素数，则
【q/p】*【p/q】=(-1)^{(p-1)*(q-1)/4}.
说明：补充资料仅用于学习参考，请勿用于其它任何用途。