BdMO National 2013: Higher Secondary 4

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BdMO
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BdMO National 2013: Higher Secondary 4

Unread post by BdMO » Fri Jan 10, 2014 1:42 am

If the fraction $\dfrac{a}{b}$ is greater than $\dfrac{31}{17}$ in the least amount while $b<17$, find $\dfrac{a}{b}$.

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SANZEED
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Re: BdMO National 2013: Higher Secondary 4

Unread post by SANZEED » Wed Jan 29, 2014 7:45 pm

Is it enough to find the successor term of $\frac{14}{17}$ in fairy sequence $f_{17}$?
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*Mahi*
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Re: BdMO National 2013: Higher Secondary 4

Unread post by *Mahi* » Wed Jan 29, 2014 9:00 pm

By the definition of Farey sequence, yes. But that too involves manual search for a primitive solution of a linear diophantine equation.
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SANZEED
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Re: BdMO National 2013: Higher Secondary 4

Unread post by SANZEED » Sun Feb 02, 2014 9:57 pm

I got $\frac{11}{6}$. Is it the answer?
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Re: BdMO National 2013: Higher Secondary 4

Unread post by photon » Mon Feb 03, 2014 1:03 pm

$\frac {11}{6} $ is the answer , I had found it by trial and error method .
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Ismail Rifat
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Re: BdMO National 2013: Higher Secondary 4

Unread post by Ismail Rifat » Fri Feb 07, 2014 12:01 am

I used Continued Fraction. And got $\frac{11}{6}$. Is it one from the right ways?

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