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Balkan MO
2016 Balkan MO
1
Injective Function
Injective Function
Source: Balkan MO 2016, Problem 1
May 7, 2016
function
algebra
Problem Statement
Find all injective functions
f
:
R
→
R
f: \mathbb R \rightarrow \mathbb R
f
:
R
→
R
such that for every real number
x
x
x
and every positive integer
n
n
n
,
∣
∑
i
=
1
n
i
(
f
(
x
+
i
+
1
)
−
f
(
f
(
x
+
i
)
)
)
∣
<
2016
\left|\sum_{i=1}^n i\left(f(x+i+1)-f(f(x+i))\right)\right|<2016
i
=
1
∑
n
i
(
f
(
x
+
i
+
1
)
−
f
(
f
(
x
+
i
))
)
<
2016
(Macedonia)
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