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1990 IMO Longlists
66
Find all continuous functions - ILL 1990 POL4
Find all continuous functions - ILL 1990 POL4
Source:
September 18, 2010
function
limit
trigonometry
algebra solved
algebra
Problem Statement
Find all the continuous bounded functions
f
:
R
→
R
f: \mathbb R \to \mathbb R
f
:
R
→
R
such that
(
f
(
x
)
)
2
−
(
f
(
y
)
)
2
=
f
(
x
+
y
)
f
(
x
−
y
)
for all
x
,
y
∈
R
.
(f(x))^2 -(f(y))^2 = f(x + y)f(x - y) \text{ for all } x, y \in \mathbb R.
(
f
(
x
)
)
2
−
(
f
(
y
)
)
2
=
f
(
x
+
y
)
f
(
x
−
y
)
for all
x
,
y
∈
R
.
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