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Saint Petersburg Mathematical Olympiad
2001 Saint Petersburg Mathematical Olympiad
11.6
11.6
Part of
2001 Saint Petersburg Mathematical Olympiad
Problems
(1)
Integer FE from St. Petersburg
Source: St. Petersburg MO 2001, 11th grade, P6
4/24/2023
Find all functions
f
:
Z
ā
Z
f:\mathbb{Z}\rightarrow\mathbb{Z}
f
:
Z
ā
Z
such that for any
x
,
y
x,y
x
,
y
the following is true:
f
(
x
+
y
+
f
(
y
)
)
=
f
(
x
)
+
2
y
f(x+y+f(y))=f(x)+2y
f
(
x
+
y
+
f
(
y
))
=
f
(
x
)
+
2
y
[I]proposed by F. Petrov
algebra
functional equation
function