MEMO 2010 ekipno problem 8
Dodao/la:
arhivaApril 28, 2012 We are given a positive integer

which is not a power of two. Show that ther exists a positive integer

with the following two properties:
(a)

is the product of two consecutive positive integers;
(b) the decimal representation of

consists of two identical blocks with

digits.
%V0
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.
Source: Srednjoeuropska matematička olimpijada 2010, ekipno natjecanje, problem 8