几类超椭圆丢番图方程组的解  

Solutions to Hyperelliptic Diophantine Equations

作　　者：高显文[1] 邓淙[1] 

机构地区：[1]昭通学院数学系,云南昭通657000

出　　处：《曲靖师范学院学报》2013年第3期9-11,共3页Journal of Qujing Normal University

基　　金：国家自然科学基金资助项目(11061028);云南省应用基础研究基金资助项目(2010CD086)

摘　　要：利用初等方法及超椭圆丢番图方程x4-Dy2=1的解与Pell方程基本解的关系,研究由两个超椭圆方程x4-D1y2=1和y4-D2z2=1构成的方程组,证明了该方程组至多只有一组正整数解;对于D1,D2的四类取值,给出了其唯一正整数解的求解公式.本文结果还说明,有无穷多个非平方的正整数D1,D2,使该方程组有正整数解.The equation set of hyperelliptic and was researched through the primary method and relation of solutions to hyperelliptic Diophantine equation and the fundamental solution of Pell equation,which proved that the equations only has a positive integer solutions.For the value of,unique integer solution formula is obtained.The results also showed that there are infinitely positive integers of non square so that the equation set has a positive integer solution.

关 键 词：超椭圆方程 丢番图方程组 PELL方程 基本解 公式解 

分 类 号：O156.7[理学—数学]