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2021 IMO Shortlist
N1
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2021 IMO Shortlist
Problems
(1)
cubefree divisibility
Source: 2021 ISL N1
7/12/2022
Find all positive integers
n
≥
1
n\geq1
n
≥
1
such that there exists a pair
(
a
,
b
)
(a,b)
(
a
,
b
)
of positive integers, such that
a
2
+
b
+
3
a^2+b+3
a
2
+
b
+
3
is not divisible by the cube of any prime, and
n
=
a
b
+
3
b
+
8
a
2
+
b
+
3
.
n=\frac{ab+3b+8}{a^2+b+3}.
n
=
a
2
+
b
+
3
ab
+
3
b
+
8
.
number theory
IMO Shortlist
Divisibility
cubefree
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