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I_n is set of solutions x^2 −2xy+y^2−4^n = 0 , where y \in I_{n-1}

Source: ITAMO 1987 p4

February 2, 2020
equationSetsalgebra

Problem Statement

Given I0={−1,1}I_0 = \{-1,1\}, define InI_n recurrently as the set of solutions xx of the equations x2−2xy+y2−4n=0x^2 -2xy+y^2- 4^n = 0, where yy ranges over all elements of In−1I_{n-1}. Determine the union of the sets InI_n over all nonnegative integers nn.
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