prove no perfet square exists

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 ...

3 Answers

62
Lokesh Verma ·

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)

1
adroit ·

thank you for the proof..

62
Lokesh Verma ·

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....

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