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2013 IMO Shortlist
A5
A5
Part of
2013 IMO Shortlist
Problems
(1)
IMO Shortlist 2013, Algebra #5
Source: IMO Shortlist 2013, Algebra #5
7/9/2014
Let
Z
≥
0
\mathbb{Z}_{\ge 0}
Z
≥
0
be the set of all nonnegative integers. Find all the functions
f
:
Z
≥
0
→
Z
≥
0
f: \mathbb{Z}_{\ge 0} \rightarrow \mathbb{Z}_{\ge 0}
f
:
Z
≥
0
→
Z
≥
0
satisfying the relation
f
(
f
(
f
(
n
)
)
)
=
f
(
n
+
1
)
+
1
f(f(f(n))) = f(n+1 ) +1
f
(
f
(
f
(
n
)))
=
f
(
n
+
1
)
+
1
for all
n
∈
Z
≥
0
n\in \mathbb{Z}_{\ge 0}
n
∈
Z
≥
0
.
function
algebra
functional equation
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