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Special Integers

Source: Junior Olympiad of Malaysia 2013 P2

July 20, 2015
number theory

Problem Statement

Find all positive integers a∈{1,2,3,4}a\in \{1,2,3,4\} such that if b=2ab=2a, then there exist infinitely many positive integers nn such that aa…aa⏟2n−bb…bb⏟n\underbrace{aa\dots aa}_\textrm{$2n$}-\underbrace{bb\dots bb}_\textrm{$n$} is a perfect square.
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