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计算标准佩尔方程x^2-Dy^2=1的最小解的vb程序

ysr2857 发布于 2025-04-04 23:43, 1066 次点击
Private Sub Command1_Click()
'计算标准佩尔方程x^2-Dy^2=1的最小解,D的数值不能太大
Dim d, a0, r
d = Val(Text1)
a0 = Int(Sqr(d))
a1 = a0
r = Sqr(d)
p0 = a0
q0 = 1
r = 1 / (r - a1)
a1 = Int(r)
p1 = a0 * a1 + 1
q1 = a1
s1 = 1
If a1 = 2 * a0 Then
p1 = p0: q1 = q0
Else
s1 = 2
Do While Int(1 / (r - a1)) <> 2 * a0
s1 = s1 + 1
r = 1 / (r - a1)
a1 = Int(r)
  p2 = a1 * p1 + p0
q2 = a1 * q1 + q0

p0 = p1: q0 = q1
p1 = p2: q1 = q2

Loop
End If

If Val(s1) Mod 2 = 0 Then
Text2 = "最小解为: x0=" & p1 & " y0=" & q1 & " 循环节长度:" & Val(s1)
Else
Text2 = "最小解为: x0=" & 2 * p1 * p1 + 1 & " y0=" & 2 * p1 * q1 & " 循环节长度:" & Val(s1)
End If

End Sub

Private Sub Command2_Click()
Text1 = ""
Text2 = ""

End Sub
1 回复
#2
ysr28572025-04-04 23:45
D的值小于等于1001,否则就溢出了!D的值必须为非平方数:
输入45,输出:最小解为: x0=161 y0=24 循环节长度:6
输入97,输出:最小解为: x0=62809633 y0=6377352 循环节长度:11
输入997,输出:最小解为: x0=14418057673 y0=456624468 循环节长度:13
输入1001,输出:最小解为: x0=1060905 y0=33532 循环节长度:14
1