1) number of positive integer solution
正整数解数
1.
So we got the counting formula of number of positive integer solution of Diophantine equation 4x_1+3x_2+2x_3=n(n≥9).
利用正整数n的一类特殊的3分拆n=n1+n2+n3,n1>n2>n3≥1,且n2+n3>n1的Ferrers图将不定方程4x1+3x2+2x3=n(n≥9)的正整数解与这种分拆联系起来,从而得到了该不定方程的正整数解数公式;同时也给出了正整数n的一类4分拆的计数公式。
2) 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。
3) positive integer solution
正整数解
1.
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
2.
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
3.
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
4) positive integer solutions
正整数解
1.
The Positive Integer Solutions of the Indefinite Equationx~2+(k-1)y~2=kz~2 & x~(k+2)-x~k =py~k;
不定方程x~2+(k-1)y~2=kz~2与x~(k+2)-x~k=py~k的正整数解
2.
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
3.
An equation involving the Euler function and the Smarandache ceil function of k order and its positive integer solutions
一个包含Euler函数及k阶Smarandache ceil函数的方程及其正整数解
5) solution of positive integer
整正数解
6) integer solution
正整数解
1.
Using the elementary methods,it was studied that the solutions of the equation Zw(Z(n))-Z(Zw(n))=0,and it was proved that the equation has infinite positive integer solutions.
用初等方法研究了方程Zw(Z(n))-Z(Zw(n))=0的可解性,并证明了该方程有无穷多个正整数解。
2.
In this paper we prove that if b■1(mod 16),b2+1=2c,b and c are both odd primes,then the equation x2+by=cz has only the positive integer solution(x,y,z)=(a,2,2).
如果b■1(mod 16),b2+1=2c,b,c都是奇素数,则方程x2+by=cz只有一个正整数解(x,y,z)=(a,2,2)。
3.
With the help of the theory of number, this dissertation shows that the Diophantine Equations X 5 ± X 3=DY 3 has integer solutions when D=P≡3,5(mod9), D=2P≡2,3(mod9) and D=4P≡2,3,5(mod6).
利用数论方法获得了丢番图方程x5-x3 =Dy3 有正整数解的充要条件 ,证明了当p为素数时 ,方程在D =P≡ 3 ,5 (mod9)时 ,仅有正整数解 (p ,x ,y) =(3 ,2 ,2 ) ,(3 ,5 ,10 ) ;在D =2P ,p≡ 2 ,3 (mod9)时 ,仅有正整数解 (p ,x ,y) =(3 ,7,14 ) ;在D =4P ,p≡ 2 ,3 ,5 (mod6)时 ,仅有正整数解 (p ,x ,y) =(2 ,3 ,3 ) ,(17,1163 ,14 695 3 8)。
补充资料：正整数
即“自然数”(1159页)。
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