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Problems
Contests
National and Regional Contests
Switzerland Contests
Switzerland - Final Round
2019 Switzerland - Final Round
6
6
Part of
2019 Switzerland - Final Round
Problems
(1)
f(m + f(n)) = f(m) - n
Source: Switzerland - 2019 Swiss MO Final Round p6
12/30/2022
Show that there exists no function
f
:
Z
→
Z
f : Z \to Z
f
:
Z
→
Z
such that for all
m
,
n
∈
Z
m, n \in Z
m
,
n
∈
Z
f
(
m
+
f
(
n
)
)
=
f
(
m
)
−
n
.
f(m + f(n)) = f(m) - n.
f
(
m
+
f
(
n
))
=
f
(
m
)
−
n
.
algebra
functional
functional equation