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Cono Sur Olympiad
1998 Cono Sur Olympiad
4
Find all functions
Find all functions
Source: Cono sur Olympiad 1998 P4(Brazil)
October 9, 2017
function
algebra
Problem Statement
Find all functions
R
−
−
>
R
R-->R
R
−
−
>
R
such that:
f
(
x
2
)
−
f
(
y
2
)
+
2
x
+
1
=
f
(
x
+
y
)
f
(
x
−
y
)
f(x^2) - f(y^2) + 2x + 1 = f(x + y)f(x - y)
f
(
x
2
)
−
f
(
y
2
)
+
2
x
+
1
=
f
(
x
+
y
)
f
(
x
−
y
)
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