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 Powerful Divisor (Posted on 2014-05-01)
Let us consider the expression MM+1, where M is a positive integer.

It can be verified that M=3 is the least value for which 22 divides MM+1.

Given that n is a positive integer, find the least value of M (in terms of n) for which MM+1 is divisible by 2n.

 No Solution Yet Submitted by K Sengupta No Rating

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 some examples | Comment 1 of 8
Text1.Text = ""
For n = 1 To 48
n2 = Int(2 ^ n + 0.5)
For m = 1 To 13
mm = Int(m ^ m + 0.5)
q = Int(mm / n2): r = mm - q * n2
If r = 0 Then
Text1.Text = Text1.Text & mform\$(n, "###") & mform\$(n2, "#########") & mform\$(m, "###") & mform\$(mm, "###########") & Chr(13) & Chr(10)
Exit For
End If
Next
Next

```  n     2^n   m    m^m
1        2  2          4  2        4  2          4  3        8  4        256  4       16  4        256  5       32  4        256  6       64  4        256  7      128  4        256  8      256  4        256  9      512  8   16777216 10     1024  8   16777216 11     2048  8   16777216 12     4096  8   16777216 13     8192  8   16777216 14    16384  8   16777216 15    32768  8   16777216 16    65536  8   16777216 17   131072  8   16777216 18   262144  8   16777216 19   524288  8   16777216 20  1048576  8   16777216 21  2097152  8   16777216 22  4194304  8   16777216 23  8388608  8   16777216 24 16777216  8   16777216```

 Posted by Charlie on 2014-05-01 16:28:34

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