MathDB
Problems
Contests
National and Regional Contests
South Africa Contests
South Africa National Olympiad
2005 South africa National Olympiad
2
2
Part of
2005 South africa National Olympiad
Problems
(1)
The largest fraction less than 16/23
Source: South African MO 2005 Q2
5/27/2012
Let
F
F
F
be the set of all fractions
m
/
n
m/n
m
/
n
where
m
m
m
and
n
n
n
are positive integers with
m
+
n
≤
2005
m+n\le 2005
m
+
n
≤
2005
. Find the largest number
a
a
a
in
F
F
F
such that
a
<
16
/
23
a < 16/23
a
<
16/23
.
number theory unsolved
number theory