1) 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
2) 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
3) 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。
4) 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)。
5) solution of positive integer
整正数解
6) 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。
补充资料：正整数
即“自然数”(1159页)。
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