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Middle European Mathematical Olympiad
2022 Middle European Mathematical Olympiad
7
7
Part of
2022 Middle European Mathematical Olympiad
Problems
(1)
NT FE with perfect squares
Source: MEMO 2022 T7
9/2/2022
Determine all functions
f
:
N
→
N
f : \mathbb {N} \rightarrow \mathbb {N}
f
:
N
→
N
such that
f
f
f
is increasing (not necessarily strictly) and the numbers
f
(
n
)
+
n
+
1
f(n)+n+1
f
(
n
)
+
n
+
1
and
f
(
f
(
n
)
)
−
f
(
n
)
f(f(n))-f(n)
f
(
f
(
n
))
−
f
(
n
)
are both perfect squares for every positive integer
n
n
n
.
number theory
functional equation