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{1...1}{5...5}6 is a perfect square (HOMC 2012 Q7)

Source:

July 24, 2019

number theoryPerfect Square

Problem Statement

Prove that the number

a =\overline{{1...1}{5...5}6}

is a perfect square (where

1

s are

2012

in total and

5

s are

2011

in total)