Let's write our power of 2 out as a string of digits: [math]d_nd_{n-1}\ldots d_5d_4d_3d_2d_1=d_nd_{n-1}\ldots d_5*10000+d_4d_3d_2d_1[/math]
  For a concrete example, this says we can write [math]123456789=12345*10000+6789[/math]
  We have a power of two with at least four digits, so it must be divisib...
 
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