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2
Function in Z^+
Function in Z^+
Source: Romania TST 2016 Day 5 Problem 2
June 2, 2016
function
algebra
number theory
functional equation
Problem Statement
Determine all
f
:
Z
+
→
Z
+
f:\mathbb{Z}^+ \rightarrow \mathbb{Z}^+
f
:
Z
+
→
Z
+
such that
f
(
m
)
≥
m
f(m)\geq m
f
(
m
)
≥
m
and
f
(
m
+
n
)
∣
f
(
m
)
+
f
(
n
)
f(m+n) \mid f(m)+f(n)
f
(
m
+
n
)
∣
f
(
m
)
+
f
(
n
)
for all
m
,
n
∈
Z
+
m,n\in \mathbb{Z}^+
m
,
n
∈
Z
+
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