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National and Regional Contests
China Contests
China Team Selection Test
2018 China Team Selection Test
4
Prove periodic if bounded
Prove periodic if bounded
Source: China TST 2018 Day 2 Q1
January 2, 2018
function
algebra
Problem Statement
Functions
f
,
g
:
Z
ā
Z
f,g:\mathbb{Z}\to\mathbb{Z}
f
,
g
:
Z
ā
Z
satisfy
f
(
g
(
x
)
+
y
)
=
g
(
f
(
y
)
+
x
)
f(g(x)+y)=g(f(y)+x)
f
(
g
(
x
)
+
y
)
=
g
(
f
(
y
)
+
x
)
for any integers
x
,
y
x,y
x
,
y
. If
f
f
f
is bounded, prove that
g
g
g
is periodic.
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