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SMO 2020 Open Round 1 Question 2

SMO · SMO 2020 Open Round 1

Question 2

Find the largest positive integer $x$ that satisfies the equation
$$(\lfloor x\rfloor-2020)^2+(\lceil x\rceil-2030)^2=(\lfloor x\rfloor-\lceil x\rceil+10)^2.$$
(Note: If you think that the above equation has no solution in positive integers, enter your answer as “0”.)