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2021 USMCA
26
2021 USMCA National Championship #26
2021 USMCA National Championship #26
Source:
May 9, 2021
Problem Statement
How many pairs of integers
(
a
,
b
)
(a, b)
(
a
,
b
)
satisfy
1
≤
a
<
100
1
3
1 \le a < 1001^3
1
≤
a
<
100
1
3
,
1
≤
b
<
100
1
2
1 \le b < 1001^2
1
≤
b
<
100
1
2
, and
100
1
3
∣
a
3
+
a
b
1001^3 \mid a^3 + ab
100
1
3
∣
a
3
+
ab
?
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