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Consider all integer combinations of *a*^{b}
for 2 ≤ *a*
≤ 5 and 2
≤ *b*
≤ 5:

2^{2}=4, 2^{3}=8, 2^{4}=16, 2^{5}=32

3^{2}=9, 3^{3}=27, 3^{4}=81, 3^{5}=243

4^{2}=16, 4^{3}=64, 4^{4}=256, 4^{5}=1024

5^{2}=25, 5^{3}=125, 5^{4}=625, 5^{5}=3125

If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:

4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125

How many distinct terms are in the
sequence generated by *a*^{b}
for 2 ≤ *a*
≤ 100 and 2
≤ *b*
≤ 100?

I couldn't think of any slick way to solve this problem. So, using the Large Number Arithmetic module, the following code took about 25 seconds.

Sub Euler029() Dim A As Integer, B As Integer Dim Rslt As Collection, aRslt As String Set Rslt = New Collection Dim ProcTime As Single ProcTime = Timer For A = 2 To 100 For B = 2 To 100 aRslt = LargePower(CStr(A), CStr(B)) On Error Resume Next Rslt.Add aRslt, aRslt On Error GoTo 0 Next B Next A Debug.Print Rslt.Count, Timer - ProcTime End Sub