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w_1(x) = x^2 - 1, w_{n+1}(x) = w_n(x)^2 - 1,

Source: Polish MO Recond Round 1977 p5

September 9, 2024
algebrapolynomial

Problem Statement

Let the polynomials wn w_n be given by the formulas: w_1(x) = x^2 - 1,   w_{n+1}(x) = w_n(x)^2 - 1,   (n = 1, 2, \ldots) and let aa be a real number. How many different real solutions does the equation wn(x)=a w_n(x) = a have?
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