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$M>0$ is an integer.

For every $n>-0$ the remainder for the n Fibonacci number divided by m is: $r_n = f_n mod n$.

I need to prove that in :

$((r_n,r_n+1)) = (r_0,r_1),(r_1,r_2),(r_2,r_3)...$ must be repeats of pairs

Will appreciate some guidance because I don't know where to start...

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    my teacher asked exactly this one question..2012-12-05
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    There are only so many pairs of residues mod $n$, and yet the sequence of pairs is infinite.2012-12-05
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    Where to start? At the definition: $f_{n+1}=f_n+f_{n-1}$.2012-12-05
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    @Berci I already know the definition but from there...2012-12-05

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