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Contests
National and Regional Contests
China Contests
China Team Selection Test
1990 China Team Selection Test
4
double difference square and summed up
double difference square and summed up
Source: China TST 1990, problem 4
June 27, 2005
function
algebra unsolved
algebra
Problem Statement
Number
a
a
a
is such that
∀
a
1
,
a
2
,
a
3
,
a
4
∈
R
\forall a_1, a_2, a_3, a_4 \in \mathbb{R}
∀
a
1
,
a
2
,
a
3
,
a
4
∈
R
, there are integers
k
1
,
k
2
,
k
3
,
k
4
k_1, k_2, k_3, k_4
k
1
,
k
2
,
k
3
,
k
4
such that
∑
1
≤
i
<
j
≤
4
(
(
a
i
−
k
i
)
−
(
a
j
−
k
j
)
)
2
≤
a
\sum_{1 \leq i < j \leq 4} ((a_i - k_i) - (a_j - k_j))^2 \leq a
∑
1
≤
i
<
j
≤
4
((
a
i
−
k
i
)
−
(
a
j
−
k
j
)
)
2
≤
a
. Find the minimum of
a
a
a
.
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