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Contests
National and Regional Contests
Netherlands Contests
Dutch IMO TST
2009 Dutch IMO TST
4
4
Part of
2009 Dutch IMO TST
Problems
(1)
f : Z \to Z, f(m + n) + f(mn - 1) = f(m)f(n) + 2
Source: 2009 Dutch IMO TST P4
1/10/2020
Find all functions
f
:
Z
→
Z
f : Z \to Z
f
:
Z
→
Z
satisfying
f
(
m
+
n
)
+
f
(
m
n
−
1
)
=
f
(
m
)
f
(
n
)
+
2
f(m + n) + f(mn -1) = f(m)f(n) + 2
f
(
m
+
n
)
+
f
(
mn
−
1
)
=
f
(
m
)
f
(
n
)
+
2
for all
m
,
n
∈
Z
m, n \in Z
m
,
n
∈
Z
.
functional equation
functional equation in Z
algebra