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Kvant 2020
M2613
M2613
Part of
Kvant 2020
Problems
(1)
Nice integer FE
Source: 2020 Caucasus Mathematical Olympiad Seniors Problem 4
3/16/2020
Find all functions
f
:
N
→
N
f : \mathbb{N}\rightarrow{\mathbb{N}}
f
:
N
→
N
such that for all positive integers
m
m
m
and
n
n
n
the number
f
(
m
)
+
n
−
m
f(m)+n-m
f
(
m
)
+
n
−
m
is divisible by
f
(
n
)
f(n)
f
(
n
)
.
functional equation
algebra
number theory