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Benelux Mathematical Olympiad 2016, Problem 3
Benelux Mathematical Olympiad 2016, Problem 3
Source:
May 1, 2016
algebra
functional equation
Problem Statement
Find all functions
f
:
R
→
Z
f :\Bbb{ R}\to \Bbb{Z}
f
:
R
→
Z
such that
(
f
(
f
(
y
)
−
x
)
)
2
+
f
(
x
)
2
+
f
(
y
)
2
=
f
(
y
)
⋅
(
1
+
2
f
(
f
(
y
)
)
)
,
\left( f(f(y) - x) \right)^2+ f(x)^2 + f(y)^2 = f(y) \cdot \left( 1 + 2f(f(y)) \right),
(
f
(
f
(
y
)
−
x
)
)
2
+
f
(
x
)
2
+
f
(
y
)
2
=
f
(
y
)
⋅
(
1
+
2
f
(
f
(
y
))
)
,
for all
x
,
y
∈
R
.
x, y \in \Bbb{R}.
x
,
y
∈
R
.
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