偶数不定方程解组数函数方案.doc

偶数不定方程的图解 Autocad 数组解点集图 2n=p1+p2 方程解组数函数 毎一个偶数都存在几组点集解，对于任意偶数它的解有几组，下面函数就是，但是原函数无法用一般的公式表达，我们采用函数逼近法，来大致了解它的增减性，方程解数组函数，大致可以用一下公式确定。 上图是890内所有偶数的解函数图像，更多需要超级计算机才可以运行程序。。。。。 以下是excel vba方程解程序 本程序可解950万内偶数不定方程，但是每次不可数量太多，对于小数可以把qp()函数中s值去掉一部分，运算速度可以快以些，但是也不会太快，因为运算次数成几何级递增。。。难度比素数筛选难得太多。。。以上方程解函数也是通过程序求解后归纳出来的，下面函数QZ(N)就是求方程解中有几个合条件的素数个数。解得组数为，这是解函数的原函数。SZU(N,i)是2n内第i个素数。SZ(2n)是2n内所有素数个数，BK(N,i)是解中第i个素数, 同时2n- BK(N,i) 也是方程的解。 Function SZU(N As Variant, K As Variant) As Variant Dim MyArray() As Variant Dim Arr() As String Dim Temp() As String Dim i As Variant Dim r As Variant Dim j As Variant Dim m As Variant Dim d As Variant m = N / 2 ReDim MyArray(m) For i = 1 To m MyArray(i) = pm(2 * i) Next i On Error Resume Next For j = 1 To m Temp = Filter(Arr, MyArray(j)) If UBound(Temp) 0 Then r = r + 1 ReDim Preserve Arr(1 To r) Arr(r) = MyArray(j) End If Next SZU = Arr(K) End Function Function pm(y As Variant) As Variant Dim d As Variant Dim f As Variant d = 3.14159265358979 f = nk(y) - 2 If f = -1 Then pm = 1: GoTo bb End If If f = 0 Then pm = 3: GoTo bb End If If f = 1 Then f = f: pm = 3 * f + 3 * (Sin(0.5 * d * f)) ^ 2 + (-1) ^ f: GoTo AA Else GoTo bb End If AA: pm = pm If qp(pm) = 0 Then f = f - 1: pm = 3 * f + 3 * (Sin(0.5 * d * f)) ^ 2 + (-1) ^ f: GoTo cc Else f = f: pm = 3 * f + 3 * (Sin(0.5 * d * f)) ^ 2 + (-1) ^ f: GoTo bb End If cc: pm = pm If qp(pm) = 0 Then f = f - 1: pm = 3 * f + 3 * (Sin(0.5 * d * f)) ^ 2 + (-1) ^ f: GoTo AA Else f = f: pm = 3 * f + 3 * (Sin(0.5 * d * f)) ^ 2 + (-1) ^ f: GoTo bb End If bb: pm = pm If f = -1 Then pm = 1 End If If f = 0 Then pm = 3 End If If f = 1 Then pm = pm End If