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If (9+4sqrt(5))^(n)=p+beta, where n and ...

If `(9+4sqrt(5))^(n)=p+beta`, where n and p are positive integers and `beta` is a positive proper fraction, prrove that `(1-beta)(p+beta)=1 and p` is an odd integer.

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To solve the problem, we need to prove two things: 1. \( (1 - \beta)(p + \beta) = 1 \) 2. \( p \) is an odd integer. Let's go through the solution step by step. ### Step 1: Understanding the Given Expression ...
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