在线性同余发生器中selecta，c，m
我期待在Excel中实现线性同余生成器。
我们知道，我们必须selectLCG的参数是a，c，m和Z0。
维基百科说这个
一般LCG的期限最多为m，而对于一些因素的selecta远低于此。 只有在以下情况下，LCG才能获得所有种子价值的全部期限：
m and the offset c are relatively prime, a - 1 is divisible by all prime factors of m, a - 1 is divisible by 4 if m is divisible by 4.
也，
m, 0 < m – the "modulus" a, 0 < a < m – the "multiplier" c, 0 < c < m – the "increment" Z0, 0 < Z0 < m – the "seed" or "start value"
我需要select这些值，我想Z0的初始值是10113383，其余是随机的。 那么，哪些价值具有特定的时期，并保证在那段时期内没有发生冲突呢？
我试图把一些值，a = 13，c = 911，m = 11584577，它看起来没有冲突。 但是我不确定是否违反规定。
我经常教数字理论和密码学课程，所以在VBA和Python中build立了一个程序库。 使用这些，我只需要再写一个：
Function GCD(num1 As Long, num2 As Long) As Long Dim a As Long Dim b As Long a = num1 b = num2 Dim R As Long R = 1 Do Until R = 0 R = a Mod b a = b b = R Loop GCD = a End Function Sub Helper_Factor(ByVal n As Long, ByVal p As Long, factors As Collection) 'Takes a passed collection and adds to it an array of the form '(q,k) where q >= p is the smallest prime divisor of n 'p is assumed to be odd 'The function is called in such a way that 'the first divisor found is automatically prime Dim q As Long, k As Long q = p Do While q <= Sqr(n) If n Mod q = 0 Then k = 1 Do While n Mod q ^ k = 0 k = k + 1 Loop k = k - 1 'went 1 step too far factors.Add Array(q, k) Helper_Factor n / q ^ k, q + 2, factors Exit Sub End If q = q + 2 Loop 'if we get here then n is prime - add it as a factor factors.Add Array(n, 1) End Sub Function Factor(ByVal n As Long) As Collection Dim factors As New Collection Dim k As Long Do While n Mod 2 ^ k = 0 k = k + 1 Loop k = k - 1 If k > 0 Then n = n / 2 ^ k factors.Add Array(2, k) End If If n > 1 Then Helper_Factor n, 3, factors Set Factor = factors End Function Function DisplayFactors(n As Long) As String Dim factors As Collection Dim i As Long, p As Long, k As Long Dim sfactors As Variant Set factors = Factor(n) ReDim sfactors(1 To factors.Count) For i = 1 To factors.Count p = factors(i)(0) k = factors(i)(1) sfactors(i) = p & IIf(k > 1, "^" & k, "") Next i DisplayFactors = Join(sfactors, "*") End Function Function MaxPeriod(a As Long, c As Long, m As Long) As Boolean 'assumes 0 < a,c < m Dim factors As Collection Dim p As Long, i As Long If GCD(c, m) > 1 Then Exit Function 'with default value of False If m Mod 4 = 0 And (a - 1) Mod 4 > 0 Then Exit Function 'else: Set factors = Factor(m) For i = 1 To factors.Count p = factors(i)(0) If p < m And (a - 1) Mod p > 0 Then Exit Function Next i 'if you survive to here: MaxPeriod = True End Function
例如，在中级窗口中，您可以检查：
?maxperiod(13,911,11584577) True
所以你似乎很幸运