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Putnam 1993 A2

Source: 1993 Putnam

October 26, 2020
Putnam

Problem Statement

The sequence an of non-zero reals satisfies an2−an−1an+1=1a_n^2 - a_{n-1}a_{n+1} = 1 for n≥1n \geq 1. Prove that there exists a real number α\alpha such that an+1=αan−an−1a_{n+1} = \alpha a_n - a_{n-1} for n≥1n \geq 1.
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