MEMO 2010, Problem T-8: Existece of m
Source:
September 12, 2010
number theory proposednumber theory
Problem Statement
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.(4th Middle European Mathematical Olympiad, Team Competition, Problem 8)