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Austrian-Polish
1979 Austrian-Polish Competition
4
f (x+y)+ f (x-y)= f (3x)
f (x+y)+ f (x-y)= f (3x)
Source: Austrian Polish 1979 APMC
April 26, 2020
functional equation
function
algebra
Problem Statement
Determine all functions
f
:
N
0
→
R
f : N_0 \to R
f
:
N
0
→
R
satisfying
f
(
x
+
y
)
+
f
(
x
−
y
)
=
f
(
3
x
)
f (x+y)+ f (x-y)= f (3x)
f
(
x
+
y
)
+
f
(
x
−
y
)
=
f
(
3
x
)
for all
x
,
y
x,y
x
,
y
.
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