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2023-IMOC
N2
Equation with powers and factorials
Equation with powers and factorials
Source: IMOC 2023 N2
September 9, 2023
factorial
number theory
Problem Statement
Find all pairs of positive integers
(
a
,
b
)
(a, b)
(
a
,
b
)
such that
a
b
+
b
a
=
a
!
+
b
2
+
a
b
+
1
a^b+b^a=a!+b^2+ab+1
a
b
+
b
a
=
a
!
+
b
2
+
ab
+
1
.
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