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Floor function is back, yay!

Source: European Mathematical Cup 2022, Junior Division, Problem 2

December 19, 2022
algebrafloor functionfunction

Problem Statement

Find all pairs (x,y)(x,y) of positive real numbers such that xyxy is an integer and x+y=⌊x2−y2⌋x+y = \lfloor x^2 - y^2 \rfloor.
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