Consider a question, that $\overline{xyxyxyxy}$ cannot be a perfect square. How should i tackle this problem. All i use is it must be $0,1 ($mod $3,4)$ and then the math, are there any another beatiful ways because this method does not work everytime.
Thank you for your time.
Your number is $xy \cdot 1010101$. Can you find a factor that cannot be repeated?