## BdMO National 2013: Higher Secondary 4

Discussion on Bangladesh Mathematical Olympiad (BdMO) National
BdMO
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### BdMO National 2013: Higher Secondary 4

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

SANZEED
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### Re: BdMO National 2013: Higher Secondary 4

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

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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Nur Muhammad Shafiullah | Mahi

SANZEED
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### Re: BdMO National 2013: Higher Secondary 4

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

$\frac {11}{6}$ 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

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