菲波那契数列与一个不定方程的正整数解

Fibonacci series and a positive integer solution to an indeterminate equation

讨论了一个二元二次不定方程的正整数解与菲波那契数列的关系 ,利用递增构造、递减构造解的方式证明了由“魔八方”建立的一个二元二次不定方程的正整数解为菲波那契数列形式 ,最后得出 。

This article mainly discusses the relation between the positive integer solution to a binary quadratic form indeterminate equation and Fibonacci series. It is proved that the positive integer solution to a binary quadratic form indeterminate equation is in the form of Fibonacci series with the methods of increase progressively structural solution and decrease progressively structural solution. And it is concluded that this equation has only a positive integer solution in the form of Fibonacci series.