摘要
研究了丢番图方程ｘ~ｙ－ｙ~ｘ＝ｌ（ｌ∈Ｎ）的自然数解的情况．通过分类考查，我们首先给出了与所给的方程的解密切相关的集合 Ｉ，然后证明了函数 Ｈ（ｘ，ｙ）在 Ｉ上关于ｘ（或ｙ）的单调性质，最后给出了原方程的非平凡解的一个十分简单的上界，从而从理论上解决了该方程的求解问题．
The positive integer solutions for Diophantine equation ｘ~ｙ－ｙ~ｘ＝ｌ（ｌ∈Ｎ） have been studied in this paper. First,a set I= { (x,y) | H(x,y) =xy-yz>0,y/1,x, y∈N} is given by classification then the monotonous character about x(or y) of function H(x,y) in I is proved,finally a very simple upper bound of the non--ordinary solutions for eguation is given. Thus the solving problem for the equation is overcome theoretically.
关键词
丢番图方程
集合
单调性
上界
正整数解
Diophantine equation Set Monotonous character Upper bound
