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National and Regional Contests
Iran Contests
Iran Team Selection Test
2008 Iran Team Selection Test
11
11
Part of
2008 Iran Team Selection Test
Problems
(1)
Find all functions
Source: Iran TST 2008
7/5/2008
k
k
k
is a given natural number. Find all functions
f
:
N
→
N
f: \mathbb{N}\rightarrow\mathbb{N}
f
:
N
→
N
such that for each
m
,
n
∈
N
m,n\in\mathbb{N}
m
,
n
∈
N
the following holds: f(m)\plus{}f(n)\mid (m\plus{}n)^k
function
modular arithmetic
number theory
relatively prime
functional equation