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1985 IMO Longlists
96
Determine all functions : f(x + y) + f(x - y) = 2f(x)f(y)
Determine all functions : f(x + y) + f(x - y) = 2f(x)f(y)
Source:
September 14, 2010
function
limit
algebra unsolved
algebra
Problem Statement
Determine all functions
f
:
R
→
R
f : \mathbb R \to \mathbb R
f
:
R
→
R
satisfying the following two conditions:(a)
f
(
x
+
y
)
+
f
(
x
−
y
)
=
2
f
(
x
)
f
(
y
)
f(x + y) + f(x - y) = 2f(x)f(y)
f
(
x
+
y
)
+
f
(
x
−
y
)
=
2
f
(
x
)
f
(
y
)
for all
x
,
y
∈
R
x, y \in \mathbb R
x
,
y
∈
R
, and(b)
lim
x
→
∞
f
(
x
)
=
0
\lim_{x\to \infty} f(x) = 0
lim
x
→
∞
f
(
x
)
=
0
.
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