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Solve x*[x]+2022=[x^2]

Source: 2022 Turkey JBMO TST P2

March 15, 2022
algebrafloor function

Problem Statement

For a real number aa, [a][a] denotes the largest integer not exceeding aa. Find all positive real numbers xx satisfying the equation xā‹…[x]+2022=[x2]x\cdot [x]+2022=[x^2]
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