02 Sep '13 07:46

1 = 1 x 1

111 = 3 x 37

111, 111, 111 = 9 x 12,345,679

111.....1 (27 1's) = 27 x 4,115,226,337,448,559,670,781,893

So it seems that it you have n 1's in a row, the number is a multiple of n.. if.. and only if?.. n is 3^0, 3^1, 3^2, 3^3 etc. It holds true for n = 3^4 = 81 too. And there are no small values of n that would not be powers of 3 for which 111...1, n 1's, would be a multiple of n.

How about big values of n?

111 = 3 x 37

111, 111, 111 = 9 x 12,345,679

111.....1 (27 1's) = 27 x 4,115,226,337,448,559,670,781,893

So it seems that it you have n 1's in a row, the number is a multiple of n.. if.. and only if?.. n is 3^0, 3^1, 3^2, 3^3 etc. It holds true for n = 3^4 = 81 too. And there are no small values of n that would not be powers of 3 for which 111...1, n 1's, would be a multiple of n.

How about big values of n?