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Possible Duplicate:
Recurrence relation, Fibonacci numbers

could someone possibly help me prove. thankyou.

$(a)$ Consider the recurrence relation $a_{n+2}a_n = a^2 _{n+1} + 2$ with $a_1 = a_2 = 1$.

prove $a_n$ and $a_{n+1}$ are coprime for $n \in \mathbb N$

so far i have:

$a_1 = a_2 = 1$

$a_3 = 3$

$a_4 = 11$

$a_5 = 41$

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    have you tried using induction?2012-11-20
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    yup but it ended up gettin really messy and i got more confused then anything, im assuming the best way would be by contradiction?2012-11-20
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    james: please see the question linked above as a duplicate: your question is asked and addressed in that post.2012-11-20
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    thankyou i just skimmed through that and it is the same question, ive completed all the sections, however, cant seem to prove why they're coprime?2012-11-20
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    james, see also http://math.stackexchange.com/questions/240724/fibonacci-question?lq=12012-11-20

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