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2022 CMIMC
2.6 1.3
2022 Alg/NT Div 1 P3 (Div 2 P6)
2022 Alg/NT Div 1 P3 (Div 2 P6)
Source:
February 28, 2022
algebra
number theory
Problem Statement
Find the smallest positive integer
N
N
N
such that each of the
101
101
101
intervals
[
N
2
,
(
N
+
1
)
2
)
,
[
(
N
+
1
)
2
,
(
N
+
2
)
2
)
,
⋯
,
[
(
N
+
100
)
2
,
(
N
+
101
)
2
)
[N^2, (N+1)^2), [(N+1)^2, (N+2)^2), \cdots, [(N+100)^2, (N+101)^2)
[
N
2
,
(
N
+
1
)
2
)
,
[(
N
+
1
)
2
,
(
N
+
2
)
2
)
,
⋯
,
[(
N
+
100
)
2
,
(
N
+
101
)
2
)
contains at least one multiple of
1001.
1001.
1001.
Proposed by Kyle Lee
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