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National and Regional Contests
Iran Contests
Iran MO (3rd Round)
2023 Iran MO (3rd Round)
2
Two random bijections
Two random bijections
Source: Iran MO 3rd round 2023 , D1P2
August 16, 2023
algebra
Problem Statement
Does there exist bijections
f
,
g
f,g
f
,
g
from positive integers to themselves st:
g
(
n
)
=
f
(
1
)
+
f
(
2
)
+
⋅
⋅
⋅
+
f
(
n
)
n
g(n)=\frac{f(1)+f(2)+ \cdot \cdot \cdot +f(n)}{n}
g
(
n
)
=
n
f
(
1
)
+
f
(
2
)
+
⋅
⋅
⋅
+
f
(
n
)
holds for any
n
n
n
?
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