In this paper,structured of generative function method and technique is introduced by finding the solution of a kind of diophantus equation,thus we introduce power series such as generative function to apply in combination probabicity.
通过求解一类丢番图方程解的个数,介绍了生成函数的构造方法和技巧,从而以幂级数作为生成函数,介绍了它在组合概率计算中的应用。
On the Diophantine equation x~p-1=Dy~n;
关于丢番图方程x~p-1=Dy~n
On the solution of the Diophantine equations x~2-2p=y~n;
关于丢番图方程x~2-2p=y~n的解
On the Diophantine equation(15n)~x+(112n)~y=(113n)~z;
关于丢番图方程(15n)~x+(112n)~y=(113n)~z
On the Diophantine equations x~4±y~6=z~2 and x~2+y~4=z~6;
关于丢番图方程x~4±y~6=z~2与x~2+y~4=z~6
When p is a odd prime and p ≠1 (mod 8), we get all solutions of diophantine equations ( x(x+1)(2x+1)=2p~ky~(2n) ) with elementary theory of number.
若p为奇素数,且p≠1(mod8)时,本文给出了丢番图方程x(x+1)(2x+1)=2pky2n的所有正整数解,并给出了Lucas猜想的一个简单证明。
With the help of the elementary theory of number and Fermat method of infinite descent,some necessary conditions have been proved provided that the Diophantine equations x 4+mx 2y 2+ny 4=z 2 has positive Integer solutions that fit (x,y) =1 m.
利用数论方法及Fermat无穷递降法 ,证明了丢番图方程x4 +mx2 y2 +ny4 =z2 在 (m ,n) =(± 6,-3 ) ,(6,3 ) ,(± 3 ,3 ) ,(-12 ,2 4) ,(± 12 ,-2 4) ,(± 6,15 ) ,(-6,-15 ) ,(3 ,6)仅有平凡整数解 ,并且获得了方程在 (-6,3 ) ,(12 ,2 4) ,(3 ,-6) ,(-6,3 3 )时的无穷多组正整数解的通解公式 ,从而完善了Aubry等人的结
Let p>3 be a prime integer prime,when the elementary grade method and the Diophantus Equation theories are used.
设p>3为素数,证明了丢番图方程x6-y6=2pz2无正整数解,证明了丢番图方程x6+y6=2pz2在p 1(mod24)时无正整数解,同时获得了方程在p≡1(mod24)时有正整数解的计算公式。
In this paper two theorems are given by using matrixvector description of polynomial multiplication, which are useful to resolve the Diophantus equation.
采用多项式乘积的矩阵－向量表示方法，证明了对求解丢番图方程极为有用的定理１和定理２，从丢番图方程的基本解法着手，给出了各种设计要求下的极点配置算法。
Diophantus OF ALEXANDRIA
丢番图(亚历山大里亚的)(活动时期250年)
Sequential and Parallel Algorithms for Solving Linear Diophantine Equations
求解线性丢番图方程(组)的串、并行算法
On the Diophantine Equation of a~x-b~(2y)=46~2;
丢番图方程a~x-b~(2y)=46~2的一解
Diophantine Equation x~3-y~6=pz~2 and Tijdeman Corijecture;
丢番图方程x~3-y~6=pz~2与Tijdeman猜想
On Integer Solution of A Diophantine Equation;
关于丢番图方程x~2-py~4=1
On the Diophantine Equation x~3±p~(3n)=Dy~2;
关于丢番图方程x~3+p~(3n)=Dy~2的讨论
About the Diophantine Equation X + mY4= Z;
关于丢番图方程x~4+my~4=z~4
On the Diophantine Equation x~3 ±5~6 =Dy~2;
关于丢番图方程x~3±5~6=Dy~2
On the Conjecture (I) of Diophantus Approximation;
关于丢番图逼近中的一个猜想(I)
On the Diophantine Equations X~5 ± X~3 = DY~3;
关于丢番图方程X~5±X~3=Dy~3
On the Diophantine Equation x~4+mx~2y~2+ny~4=z~2;
关于丢番图方程x~4+mx~2y~2+ny~4=z~2
On the Diophantine Equations x~2±y~4=z~3;
关于丢番图方程x~2±y~4=z~3
On the Diophantine Equations x(x+1)=Dy~4;
关于丢番图方程x(x+1)=Dy~4
On the Diophantine Equation (x~m-1)(x~(mn) -1)=y~2;
关于丢番图方程(x~m-1)(x~(mn)-1)=y~2
On the Diophantine Equations x_4±y_6=z_2;
关于丢番图方程x~4±y~6=z~2
On the Diophantine Equations x~3±y~6=z~2;
关于丢番图方程x~3±y~6=z~2的解
On the Sum of Equal Powers and Diophantine Equation S_5(x) =y~n;
关于幂和丢番图方程S_5(x)=y~n
On the Diophantine Equation x~6±y~6=pqDz~2;
关于丢番图方程x~6±y~6=pqDz~2