关于丢番图方程x^3-y^6=3pz^2及其计算程序  

On the diophantine equation x^3-y^6=3pz^2

作　　者：王云葵[1] 唐荣保 

机构地区：[1]广西民族学院计算机与信息科学学院,广西南宁530006 [2]广西灌阳县新桥中学,广西桂林541604

出　　处：《湖南理工学院学报（自然科学版）》2004年第3期6-10,共5页Journal of Hunan Institute of Science and Technology(Natural Sciences)

摘　　要：设p≡ 5 (mod6 )为素数 ,证明了丢番图方程x3 -y6=3pz2 在p≡ 5 (mod12 )为素数时均无正整数解 ,在p≡ 11(mod12 )为素数时均有无穷多组正整数解 ,并且还获得了该方程全部正整数解的通解公式 ,同时编写了计算正整数解的计算程序 ,可以很方便地计算该方程的正整数解。Supposing p is prime (x 3-y 6=3pz 2), this thesis proved that the diophantine equation had no positive integer solution as well as which is prime. Thesis also proved that the equation had a lot of teams positive integer solution while which was prime, and get the general expressions for all positive integer solutions of the Diophantine Equation. In addition, the thesis designed the computing program for positive integer solutions, to compute the positive integer solutions of this Equation conveniently.

关 键 词：丢番图方程 TIJDEMAN猜想 广义FERMAT猜想 计算程序 

分 类 号：O173[理学—数学]