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