- #1

Ackbach

Gold Member

MHB

- 4,155

- 89

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Consider the power series expansion

\[\frac{1}{1-2x-x^2} = \sum_{n=0}^\infty a_n x^n.\]

Prove that, for each integer $n\geq 0$, there is an integer $m$ such that

\[a_n^2 + a_{n+1}^2 = a_m .\]

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