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2
Functional equation
Functional equation
Source: Indian Team Selection Test 2015 Day 2 Problem 2
July 11, 2015
algebra
functional equation
function
Problem Statement
Find all functions from
N
∪
{
0
}
→
N
∪
{
0
}
\mathbb{N}\cup\{0\}\to\mathbb{N}\cup\{0\}
N
∪
{
0
}
→
N
∪
{
0
}
such that
f
(
m
2
+
m
f
(
n
)
)
=
m
f
(
m
+
n
)
f(m^2+mf(n))=mf(m+n)
f
(
m
2
+
m
f
(
n
))
=
m
f
(
m
+
n
)
, for all
m
,
n
∈
N
∪
{
0
}
m,n\in \mathbb{N}\cup\{0\}
m
,
n
∈
N
∪
{
0
}
.
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