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(China) National High School Mathematics League
2023 China Second Round
11
11
Part of
2023 China Second Round
Problems
(1)
China Second Round Olympiad 2023 Test 1 Q 11
Source: Sep 10, 2023
9/10/2023
Find all real numbers
t
t
t
not less than
1
1
1
that satisfy the following requirements: for any
a
,
b
∈
[
−
1
,
t
]
a,b\in [-1,t]
a
,
b
∈
[
−
1
,
t
]
, there always exists
c
,
d
∈
[
−
1
,
t
]
c,d \in [-1,t ]
c
,
d
∈
[
−
1
,
t
]
such that
(
a
+
c
)
(
b
+
d
)
=
1.
(a+c)(b+d)=1.
(
a
+
c
)
(
b
+
d
)
=
1.
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