MEMO 2010 ekipno problem 8


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April 28, 2012
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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.
Source: Srednjoeuropska matematička olimpijada 2010, ekipno natjecanje, problem 8