We are given a positive integer
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
which is not a power of two. Show that ther exists a positive integer
![m](/media/m/1/3/6/1361d4850444c055a8a322281f279b39.png)
with the following two properties:
(a)
![m](/media/m/1/3/6/1361d4850444c055a8a322281f279b39.png)
is the product of two consecutive positive integers;
(b) the decimal representation of
![m](/media/m/1/3/6/1361d4850444c055a8a322281f279b39.png)
consists of two identical blocks with
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
digits.
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We are given a positive integer $n$ which is not a power of two. Show that ther exists a positive integer $m$ with the following two properties:
(a) $m$ is the product of two consecutive positive integers;
(b) the decimal representation of $m$ consists of two identical blocks with $n$ digits.