Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.


Ciekaw
Posts:
19
Registered:
11/24/12


Re: Generating coprime pairs
Posted:
Dec 2, 2012 11:46 AM


On Sunday, December 2, 2012 4:05:25 PM UTC+1, Leon Aigret wrote:
> Oops. Looking again, I see that the actual representation is > > [0; 1, 1, 1, 3, 3], so the link between the Cbit series and the > > continued fraction representation of the ratio of the coprime pair > > requires some modif1cation at both ends. Still think that the approach > > is basically sound. >
This is connection to the Euclidean algorithm.
Euclidean algorithm:
i a(i) b(i) Cbit(i) 0 36 23 1 13 23 1 2 13 10 1 3 3 10 1 4 3 7 0 5 3 4 0 6 3 1 1 7 2 1 0 8 1 1 1
Table formula: if min[a(i1);b(i1)] = max[a(i);b(i)] then Cbit(i)=1 if min[a(i1);b(i1)] = min[a(i);b(i)] then Cbit(i)=0
if a(i1)=max[a(i1);b(i1)] then a(i)=a(i1)b(i1) else a(i)=a(i1); if b(i1)=max[a(i1);b(i1)] then b(i)=b(i1)a(i1) else b(i)=b(i1);



