丢番图方程x^4-Dy^2=1的几类可解情形和求解公式  

Some kinds of solvable cases and solving formulas for Diophantine equation x^4-Dy^2=1

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：《高师理科学刊》2013年第4期33-35,共3页Journal of Science of Teachers＇College and University

摘　　要：利用初等方法及方程x^4-Dy^2=1的解与Pell方程基本解的关系,找到使x^4-Dy^2=1有正整数解的8类D值,并给出求解公式.当D=1 785,7 140,28 560时,能求出方程的一组解,对所给的其它D值,能求出方程的唯一解.结果表明,有无穷多个非平方的正整数D使方程x^4-Dy^2=1有正整数解.To quartic Diophantine equation x4-Dy2=1,found eight kind values of D that make x4-Dy2=1 to have positive integer solutions by elementary method and relation between the solutions of the Diophantine equation and the basic solutions of Pell equation,furthermore gave solving formulas.Gave one group solution when D=1 785,7 140,28 560,and can find its unique solution for other D.The conclusion indicated that there exist infinite non-square positive integer D to make the equation have positive integer solutions.

关 键 词：丢番图方程 PELL方程 基本解 公式解 

分 类 号：O156.7[理学—数学]