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IMO Shortlist 2013, Number Theory #4

Source: IMO Shortlist 2013, Number Theory #4

July 10, 2014
number theoryPerfect Squaredecimal representationIMO ShortlistHi

Problem Statement

Determine whether there exists an infinite sequence of nonzero digits a1,a2,a3,⋯a_1 , a_2 , a_3 , \cdots and a positive integer NN such that for every integer k>Nk > N, the number akak−1⋯a1‾\overline{a_k a_{k-1}\cdots a_1 } is a perfect square.
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