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MEMO 2010, Problem T-8: Existece of m

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September 12, 2010
number theory proposednumber theory

Problem Statement

We are given a positive integer nn which is not a power of two. Show that ther exists a positive integer mm with the following two properties: (a) mm is the product of two consecutive positive integers; (b) the decimal representation of mm consists of two identical blocks with nn digits.
(4th Middle European Mathematical Olympiad, Team Competition, Problem 8)