X^2+XY-Y^2+k=0正整数解的条件

The Conditions for the Positive Integer Solutions of the Equation X^2+XY-Y^2+k=0

方程X2+XY-Y2+k=0具有Fibonacci数列的正整数解,并且方程X2+XY-Y2+k=0具有Fibonacci数列的正整数解时满足一定约束条件.Lucas数列实际上是一种广义Fibonacci数列.方程X2+X-1=0的正整数解也与Fibonacci数列有关.

The positive integer solutions of Fibonacci sequence and the condition for the positive integer solutions of the equation X^2 ＋ XY - y^2 ＋ k = 0 were studied in this paper. Lucas sequence is one of general Fibonacci sequences. The solution of the equation X^2 ＋ X - 1 = 0 has something to do with Fibonacci sequences.