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Powerful Divisor (Posted on 2014-05-01) Difficulty: 3 of 5
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    
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Some Thoughts 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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