## BdMO National 2013: Higher Secondary 4

BdMO
Posts: 134
Joined: Tue Jan 18, 2011 1:31 pm

### 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
Posts: 550
Joined: Wed Dec 28, 2011 6:45 pm

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

Is it enough to find the successor term of $\frac{14}{17}$ in fairy sequence $f_{17}$?
$\color{blue}{\textit{To}} \color{red}{\textit{ problems }} \color{blue}{\textit{I am encountering with-}} \color{green}{\textit{AVADA KEDAVRA!}}$

*Mahi*
Posts: 1175
Joined: Wed Dec 29, 2010 12:46 pm
Location: 23.786228,90.354974
Contact:

### 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.

Use $L^AT_EX$, It makes our work a lot easier!

SANZEED
Posts: 550
Joined: Wed Dec 28, 2011 6:45 pm

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

I got $\frac{11}{6}$. Is it the answer?
$\color{blue}{\textit{To}} \color{red}{\textit{ problems }} \color{blue}{\textit{I am encountering with-}} \color{green}{\textit{AVADA KEDAVRA!}}$

photon
Posts: 186
Joined: Sat Feb 05, 2011 3:39 pm
Location: dhaka
Contact:

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

$\frac {11}{6}$ is the answer , I had found it by trial and error method .
Try not to become a man of success but rather to become a man of value.-Albert Einstein

Ismail Rifat
Posts: 1
Joined: Tue Aug 16, 2011 11:37 am

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

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