Read carefully, then post your answer.

Can you provide a simple YES or NO correct answer to the question :
Is 1010101......101 (n ones interwoven with n-1 zeroes) evenly divisible (i.e. without remainder) by 111…1(a string of n ones)?

Rem: n>1

When first seen I assumed this was binary but then considered base 10.

Having discovered a similarity of result I tried several bases between 2 and 10.  This was done in a spreadsheet but the result was as indicated by Jer. 

From that I concluded that I can provide an emphatic NO the question but if I am allowed to make a conditional response dependent upon the value of 'n' then my qualified answer is:
NO, but IF .....
              n is odd there is divisibility.
              n is even there is no divisibility.

Posted by brianjn on 2011-01-14 03:52:14