Two lemmas on linear sequences of order two


Note: My English is so bad but don’t worry about that! 🙂

A sequence (a_n) is called linear of order two if there are real numbers p,q such that a_{n+2}=pa_{n+1}+qa_n\;\forall n=1,2,3,...

In this topic we’ll use ideas in proofs of two following lemmas to solve some Olympiad problems.

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