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Find the missing digit

Source: Bundeswettbewerb Mathematik 2009 Round 1

July 29, 2018
number theorysquare

Problem Statement

Determine all possible digits zz for which 9...9⏟100z0...0⏟1009\underbrace{9...9}_{100}z\underbrace{0...0}_{100}9 is a square number.
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