the set of all positive integers

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)。

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。

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。

An equation involving the pseudo Smarandache function and its positive integer solutions;

关于伪Smarandache函数的一个方程及其正整数解

On the necessary condition of one class of hyperelliptic equations having the positive integer solutions;

一类超椭圆方程有正整数解的必要条件的问题

A function equation related to the Smarandache function and its positive integer solutions;

一个与Smarandache函数有关的函数方程及其正整数解

The equation xn+yn=zn(n>2)(The letters are all positive integer except especially mentioned) was proven by quadratic equation.

即:不定方程xn+yn=zn(n>2)(本文的各种字母没有特别指出时,都表示是正整数),当x=10a时,z不等正整数。

Let n be positive integer,f(n) here refers to the mininum mumber of 1 when n can be expressed by 1,+,× and().

设n为正整数,f(n)是可以用1以及任意多个+号和×号(以及括号)来表示n时所用1的最少的个数。

Based on the literature([1]),we apply 1+12~2+13~2+…+=π~26 to study the estimation of any subdivide numbers of a positive integer where N and the subdivide numbers allow to be disorder and repeated.

在文献[1]的基础上,应用1+122+123+…+=π26来讨论正整数N的无序允许重复的任意剖分数的估计,从而给出了正整数无序允许重复剖分数的一个较优的上界估计式。

Positive Integer Solutions of The Equation(ax~m+1)/(ax+1)=y~n;

方程(ax~m+1)/(ax+1)=y~n的正整数解

Positive Integer Solutions of the Equation (ax~m-1)/(ax-1)=y~n;

方程(αx~m-1)/(αx-1)=y~n的正整数解

The positive integer solution to the equation φ (kn) = φ ((k+1) n), (k = 1, 2, ...);

方程φ(kn)=φ((k+1)n),(k=1,2,…)的正整数解

Positive Integral Solution of Indeterminate Equation x~2-py~2=z~2

不定方程x~2-py~2=z~2的正整数解

Number for Positive Integral Solution of the Diophantine Equation mx+2y+z=n(m≥3,n≥m+3);

不定方程mx+2y+z=n(m≥3,n≥m+3)的正整数解数

On the Class Number of Positive Integer Solution of Multi-head Linear Diophantine Equation

一类多元一次不定方程的正整数解的组数问题

The Positive Integer Solutions of the Quadratic Indefinite Equation 3f~2+3fg+g~2=h~2;

二次不定方程3f~2+3fg+g~2=h~2的正整数解

A Positive Integral Solution to the Indefinite Cubic Equation with 36 Equality Signs;

具有三十六个等号的三次不定方程的正整数解

The Confirmation of Positive Integral Solution of the Indeterminate Equation 1/x+1/y=s/t;

不定方程1/x+1/y=s/t正整数解的确定

An Analysis of the Positive Integral Solution to the Indefinite Cubic Equation with 10 Equality Signs;

具有十个等号的三次不定方程的正整数解

An equation involving the functions Z(n) and D(n) and its all positive integer solutions

一个包含Z(n)和D(n)函数的方程及其它的正整数解

The Integral Solutions of the Congruence Equation for the Sum of even Exponent of The Continuous Positive Integers

连续正整数偶次幂之和同余方程的整数解

an integer or a fraction.

正整数负整数正分数负分数和零。

ECM cathode design using numerical simulated cut -and - try

基于正问题数值求解模拟“试验修整”的电解加工阴极设计

THE METHOD OF VARIATION OF PARAMETERS FOR SALVING THE RAITZIN’S CANONICAL EQUATIONS OF NONHOLONOMIC NONCONSERVATIVE MECHANICAL SYSTEMS;

求解非完整非保守力学系统Raitzin正则方程的常数变易法

An expression of a positive integer as a sum of positive integers.

正整数式用一个正整数来表示正整数总集合的表达方式

X~4+Y~4=Z~4(No Integer Solution);

X~4+Y~4=Z~4无整数解完整解法

Revised Pension Adjustment Index

养恤金订正调整指数