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2016 IMO Shortlist
A2
A2
Part of
2016 IMO Shortlist
Problems
(1)
|a_i/a_j - a_k/a_l| <= C
Source: 2016 IMO Shortlist A2
7/19/2017
Find the smallest constant
C
>
0
C > 0
C
>
0
for which the following statement holds: among any five positive real numbers
a
1
,
a
2
,
a
3
,
a
4
,
a
5
a_1,a_2,a_3,a_4,a_5
a
1
,
a
2
,
a
3
,
a
4
,
a
5
(not necessarily distinct), one can always choose distinct subscripts
i
,
j
,
k
,
l
i,j,k,l
i
,
j
,
k
,
l
such that
∣
a
i
a
j
−
a
k
a
l
∣
≤
C
.
\left| \frac{a_i}{a_j} - \frac {a_k}{a_l} \right| \le C.
a
j
a
i
−
a
l
a
k
≤
C
.
IMO Shortlist
algebra