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P(x) is a quadratic trinomial

Source: Tuymaada 2009, Junior League, First Day, Problem 2

July 19, 2009
quadraticsalgebra unsolvedalgebra

Problem Statement

P(x) P(x) is a quadratic trinomial. What maximum number of terms equal to the sum of the two preceding terms can occur in the sequence P(1) P(1), P(2) P(2), P(3) P(3), …? \dots? Proposed by A. Golovanov
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