olymmath

KöMaL 2018 K585

    Andrew wrote three (not necessarily different) positive integers on a blackboard, each of them smaller than 20182018. Then he erased these numbers (AA, BB and CC), and replaced them with A+B2,B+C2,A+C2.\frac{A+B}2, \frac{B+C}2, \frac{A+C}2. He repeated this procedure 1111 times altogether. As a result, one of the three numbers on the board is 100100. What are the other two numbers?

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