Prove that there are no perfect squares in the array below:
11 111 1111 ...
22 222 2222 ...
33 333 3333 ...
44 444 4444 ...
..
..
..
99 999 9999 ...
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UP 0 DOWN 0 0 3
3 Answers
Lokesh Verma
·2009-09-04 05:02:02
proof of 11, 111, 1111... etc is a direct consequene of 4n or 4n+1 (form of perfect square)
The rest follow from the proof of 11, 111, 111... etc.. (whichi is of the form 4n-1)
Lokesh Verma
·2009-09-05 03:19:34
i made a slight mistake in the above statement.. not all can be directly said.. most of these can be eliminated by the logic of 4n and 4n+1
the others, namely 33333.. 44444..., 777777, have to be proved seperately!
9999, 44444 is a consequence of perfect square times 1111....