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Portugal MO
2005 Portugal MO
6
f(a + b)f(a - b) = f(a^2) in N
f(a + b)f(a - b) = f(a^2) in N
Source: Portugal OPM 2005 p6
May 19, 2024
algebra
functional
functional equation
number theory
Problem Statement
Prove that there is a unique function
f
:
N
→
N
f: N\to N
f
:
N
→
N
, that verifies
f
(
a
+
b
)
f
(
a
−
b
)
=
f
(
a
2
)
f(a + b)f(a - b) = f(a^2)
f
(
a
+
b
)
f
(
a
−
b
)
=
f
(
a
2
)
, for any
a
,
b
∈
N
a, b\in N
a
,
b
∈
N
such that
a
>
b
a > b
a
>
b
.
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