# Any integer in 99, 999, 9999… sequence is not a perfect square [duplicate]

I am learning number theory and trying to understand how does below statement is true .

Show that no integer in the following sequence can be a perfect square:
99, 999, 9999, 99999, ...


## marked as duplicate by Dietrich Burde, Parcly Taxel, Smylic, Jeremy Rickard, erfinkMay 15 '17 at 9:00

Notice that all perfect squares satisfy $x^2 \equiv 0,1($mod $4)$, meaning the remainder of perfect squares when divided by $4$ is always $0$ or $1$. On the other hand, all these numbers you gave have remainder $3$ when divided by $4$, so they can't be perfect squares.