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National and Regional Contests
Romania Contests
Romania - Local Contests
Nicolae Coculescu
2007 Nicolae Coculescu
1
f(x+y)+f(x-y)=f(x)+f(y) +f(f(x+y))
f(x+y)+f(x-y)=f(x)+f(y) +f(f(x+y))
Source:
December 13, 2019
function
Find all functions
algebra
Problem Statement
Find all functions
f
:
Q
⟶
R
f:\mathbb{Q}\longrightarrow\mathbb{R}
f
:
Q
⟶
R
satisfying the equation
f
(
x
+
y
)
+
f
(
x
−
y
)
=
f
(
x
)
+
f
(
y
)
+
f
(
f
(
x
+
y
)
)
,
f(x+y)+f(x-y)=f(x)+f(y) +f(f(x+y)) ,
f
(
x
+
y
)
+
f
(
x
−
y
)
=
f
(
x
)
+
f
(
y
)
+
f
(
f
(
x
+
y
))
,
for any rational numbers
x
,
y
.
x,y.
x
,
y
.
Mihai Onucu Drîmbe
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