Question 1
We are given a positive integer $n$ which is not a power of $2$. Show that there exists a positive integer $m$ with the following two properties:
(i) $m$ is the product of two consecutive positive integers;
(ii) the decimal representation of $m$ consists of two identical blocks of $n$ digits.
(i) $m$ is the product of two consecutive positive integers;
(ii) the decimal representation of $m$ consists of two identical blocks of $n$ digits.