IMO Shortlist 1967 problem 2
Dodao/la:
arhiva2. travnja 2012. Which fractions
![\displaystyle \dfrac{p}{q},](/media/m/f/b/f/fbf5da427affeebaee117337b84c6ace.png)
where
![p,q](/media/m/0/3/4/03465730f44d7b76c3fccd5acb749aa5.png)
are positive integers
![< 100](/media/m/6/d/f/6df8660159161e8d15a444fb842e2389.png)
, is closest to
![\sqrt{2} ?](/media/m/6/2/f/62f468a6a810e5eb8fb4947058c144a4.png)
Find all digits after the point in decimal representation of that fraction which coincide with digits in decimal representation of
![\sqrt{2}](/media/m/e/e/1/ee1d57d4b54a6c9a2e2565f431cdd9da.png)
(without using any table).
%V0
Which fractions $\displaystyle \dfrac{p}{q},$ where $p,q$ are positive integers $< 100$, is closest to $\sqrt{2} ?$ Find all digits after the point in decimal representation of that fraction which coincide with digits in decimal representation of $\sqrt{2}$ (without using any table).
Izvor: Međunarodna matematička olimpijada, shortlist 1967