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Baltic Way
2011 Baltic Way
2
Prove that f is bounded if equation holds
Prove that f is bounded if equation holds
Source: Baltic Way 2011
November 6, 2011
algebra
functional equation
Problem Statement
Let
f
:
Z
→
Z
f:\mathbb{Z}\to\mathbb{Z}
f
:
Z
→
Z
be a function such that for all integers
x
x
x
and
y
y
y
, the following holds:
f
(
f
(
x
)
−
y
)
=
f
(
y
)
−
f
(
f
(
x
)
)
.
f(f(x)-y)=f(y)-f(f(x)).
f
(
f
(
x
)
−
y
)
=
f
(
y
)
−
f
(
f
(
x
))
.
Show that
f
f
f
is bounded.
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