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Distinct x, y with (x+y-1)^2 = xy+1 - Iran First Round 2018, P16

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March 7, 2021
algebraSets

Problem Statement

A subset of the real numbers has the property that for any two distinct elements of it such as xx and yy, we have (x+y−1)2=xy+1(x+y-1)^2 = xy+1. What is the maximum number of elements in this set?
<spanclass=′latex−bold′>(A)</span> 1<spanclass=′latex−bold′>(B)</span> 2<spanclass=′latex−bold′>(C)</span> 3<spanclass=′latex−bold′>(D)</span> 4<spanclass=′latex−bold′>(E)</span> Infinity<span class='latex-bold'>(A)</span>\ 1\qquad<span class='latex-bold'>(B)</span>\ 2\qquad<span class='latex-bold'>(C)</span>\ 3\qquad<span class='latex-bold'>(D)</span>\ 4\qquad<span class='latex-bold'>(E)</span>\ \text{Infinity}
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