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Austrian-Polish
1997 Austrian-Polish Competition
6
Functional equation
Functional equation
Source: Austrain Polish 1997
December 7, 2013
function
induction
algebra solved
algebra
Problem Statement
Show that there is no integer-valued function on the integers such that
f
(
m
+
f
(
n
)
)
=
f
(
m
)
ā
n
f(m+f(n))=f(m)-n
f
(
m
+
f
(
n
))
=
f
(
m
)
ā
n
for all
m
,
n
m,n
m
,
n
.
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