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2009 Pan African
2
find all f such that f(x^2-y^2)=f(x)f(y)
find all f such that f(x^2-y^2)=f(x)f(y)
Source: Pan African Olympiad 2009
October 1, 2011
function
induction
number theory proposed
number theory
Problem Statement
Find all functions
f
:
N
0
→
N
0
f:\mathbb{N}_0\to\mathbb{N}_0
f
:
N
0
→
N
0
for which
f
(
0
)
=
0
f(0)=0
f
(
0
)
=
0
and
f
(
x
2
−
y
2
)
=
f
(
x
)
f
(
y
)
f(x^2-y^2)=f(x)f(y)
f
(
x
2
−
y
2
)
=
f
(
x
)
f
(
y
)
for all
x
,
y
∈
N
0
x,y\in\mathbb{N}_0
x
,
y
∈
N
0
with
x
>
y
x>y
x
>
y
.
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