MathDB

2.

Part of JOM 2013

Problems(1)

Special Integers

Source: Junior Olympiad of Malaysia 2013 P2

7/20/2015
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.
number theory