perfect squares

This one is fairly direct and has been discussed several times..

See the question here is same as finding the number of perfect squares in the sequence ..

1, 11, 111, 1111, .....

Which the answer is 1 because except 1, none of the other numbers is in the form of 4n+1.. They are all of the form 4n+3

Every number is either even or odd.

Hence of the form 2n or 2n+1

Their square will be 4n² or 4n²+4n+1

ie Their square will be 4n² or 4(n²+n)+1

So a multiple of 4 or a multiple of 4 + 1

BUt 11, 111, 1111, etc are all of the from 8+3 or 108+3 or 1108+3 and so on..

Hence the above statement