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BdMO National 2013: Higher Secondary 4
Posted: Fri Jan 10, 2014 1:42 am
by BdMO
If the fraction $\dfrac{a}{b}$ is greater than $\dfrac{31}{17}$ in the least amount while $b<17$, find $\dfrac{a}{b}$.
Re: BdMO National 2013: Higher Secondary 4
Posted: Wed Jan 29, 2014 7:45 pm
by SANZEED
Is it enough to find the successor term of $\frac{14}{17}$ in fairy sequence $f_{17}$?
Re: BdMO National 2013: Higher Secondary 4
Posted: Wed Jan 29, 2014 9:00 pm
by *Mahi*
By the definition of Farey sequence, yes. But that too involves manual search for a primitive solution of a linear diophantine equation.
Re: BdMO National 2013: Higher Secondary 4
Posted: Sun Feb 02, 2014 9:57 pm
by SANZEED
I got $\frac{11}{6}$. Is it the answer?
Re: BdMO National 2013: Higher Secondary 4
Posted: Mon Feb 03, 2014 1:03 pm
by photon
$\frac {11}{6} $ is the answer , I had found it by trial and error method .
Re: BdMO National 2013: Higher Secondary 4
Posted: Fri Feb 07, 2014 12:01 am
by Ismail Rifat
I used Continued Fraction. And got $\frac{11}{6}$. Is it one from the right ways?