# Math Help - squared series...

1. ## squared series...

I was dealing with a problem in a book by David M. Burton.The question is :
Prove that no integer in the following sequence is a perfect square:
11,111,1111,11111,......

thanks

kaka

2. Originally Posted by kaka1988
I was dealing with a problem in a book by David M. Burton.The question is :
Prove that no integer in the following sequence is a perfect square:
11,111,1111,11111,......

thanks

kaka

Every integer squared equals $0\,\,\,or\,\,\,1\!\!\!\pmod 4$ . As none of $11,111,1111,\ldots$ is even, this means that if any of these numbers is a square then $(111\ldots 1)-1=0\!\!\!\pmod 4$ . Check that this is impossible.

Tonio