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TOT 411 1994 Spring O S2 a_{n+2}x^2 + a_{n+1}x+ a_n = 0

Source:

June 12, 2024
algebrapolynomial

Problem Statement

The sequence of positive integers a1a_1, a2a_2,...... is such that for each n=1n = 1,22, ...... the quadratic equation an+2x2+an+1x+an=0a_{n+2}x^2 + a_{n+1}x+ a_n = 0 has a real root. Can the sequence consist of (a) 1010 terms, (b) an infinite number of terms?
(A Shapovalov)