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France Contests
French Mathematical Olympiad
1995 French Mathematical Olympiad
Problem 5
bijection over N
bijection over N
Source: French MO 1995 P5
April 22, 2021
function
algebra
Problem Statement
Let
f
f
f
be a bijection from
N
\mathbb N
N
to itself. Prove that one can always find three natural number
a
,
b
,
c
a,b,c
a
,
b
,
c
such that
a
<
b
<
c
a<b<c
a
<
b
<
c
and
f
(
a
)
+
f
(
c
)
=
2
f
(
b
)
f(a)+f(c)=2f(b)
f
(
a
)
+
f
(
c
)
=
2
f
(
b
)
.
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