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Finding least number that can be left...

Source:

February 7, 2011
invariant

Problem Statement

101101 numbers are written on a blackboard: 12,22,32,⋯ ,10121^2, 2^2, 3^2, \cdots, 101^2. Alex choses any two numbers and replaces them by their positive difference. He repeats this operation until one number is left on the blackboard. Determine the smallest possible value of this number.
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