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2001 India National Olympiad
6
All functions f with f(x +y) = f(x) f(y) f(xy)
All functions f with f(x +y) = f(x) f(y) f(xy)
Source: INMO 2001 Probelm 6
October 10, 2005
function
algebra unsolved
algebra
Problem Statement
Find all functions
f
:
R
→
R
f : \mathbb{R} \to\mathbb{R}
f
:
R
→
R
such that
f
(
x
+
y
)
=
f
(
x
)
f
(
y
)
f
(
x
y
)
f(x +y) = f(x) f(y) f(xy)
f
(
x
+
y
)
=
f
(
x
)
f
(
y
)
f
(
x
y
)
for all
x
,
y
∈
R
.
x, y \in \mathbb{R}.
x
,
y
∈
R
.
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